
==== Front
Heliyon
Heliyon
Heliyon
2405-8440
Elsevier

S2405-8440(24)12445-0
10.1016/j.heliyon.2024.e36414
e36414
Research Article
Physical properties and thermodynamic characteristics of hydrogen
Levikhin A.A. levihin1981@gmail.com

Boryaev А.А. sasa1953@yandex.ru
⁎
Ustinov Baltic State Technical University “VOENMEH”, 1 Pervaya Krasnoarmeyskaya St., Saint Petersburg, 199005, Russia
⁎ Corresponding author. sasa1953@yandex.ru
19 8 2024
15 9 2024
19 8 2024
10 17 e3641414 7 2024
14 8 2024
15 8 2024
© 2024 The Authors. Published by Elsevier Ltd.
2024

https://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
This paper discusses the use of hydrogen in various industries and energy sectors. It focuses on studying the properties and characteristics of hydrogen, which serves as a key factor in determining its potential in various applications. Such aspects of hydrogen application as environmental friendliness as well as utilization efficiency and safety are considered. The widespread use of hydrogen as a universal environmentally friendly energy carrier, raw material and fuel will successfully solve many significant ecological, energy and technological problems. The most important physical and chemical properties and thermodynamic characteristics of hydrogen described in the paper make it possible to choose among existing technologies or focus on developing new ones that will ensure high efficiency of its utilization not only at present but also in future. The information presented in the paper can be used for reference.

Keywords

Hydrogen
Energy sector
Industry
Ecology
Safety
Physical properties
Thermodynamic characteristics
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pmc1 Introduction

Hydrogen is the simplest and most common element in the universe. Due to its unique properties and characteristics, hydrogen, which was long considered the fuel of the future, is now being used in a variety of industries that could revolutionize energy, transportation and manufacturing sectors.

1.1 Hydrogen utilization

One of the key characteristics of hydrogen is its versatility. It can be produced from various sources, including renewable energy sources (such as solar and wind energy) as well as fossil fuels (e.g., using steam methane reforming). This versatility allows hydrogen to contribute to decarbonization while meeting specific industrial needs. Another important characteristic of hydrogen is its high energy density. By weight, hydrogen contains more energy than gasoline, which makes it an attractive fuel for vehicles, ships, and even airplanes. Its combustion produces only water vapor, without any harmful emissions that contribute to climate change. Besides, hydrogen has unique chemical properties enabling its use in various industrial applications.

For instance, its ability to react with nitrogen at high temperatures makes it an ideal raw material for the production of ammonia, an essential component of fertilizers. In addition, its reactivity with other elements makes it quite valuable in metal refining and hydrogenation in the food and chemical industries.

However, the use of hydrogen is associated with a number of challenges. Hydrogen storage and transportation are somewhat complicated due to its low density at normal temperature. Besides, developing the infrastructure for large-scale hydrogen production requires significant investments. Despite these issues, the potential benefits of hydrogen are undeniable. Countries and industries around the world are investing resources in research and development, leading to advances in hydrogen production, storage and utilization. Here is a brief overview of how various industries are exploring the potential of using hydrogen:• Energy: Green hydrogen produced from renewable sources can be stored and used to generate electricity when needed, thus ensuring a reliable and clean source of energy. Hydrogen can be used as a universal energy “preservative” since any type of energy can be converted to hydrogen energy, stored as hydrogen, and converted back into any other type of energy required. It can be produced by water electrolysis when it is possible to obtain energy from unstable renewable sources (wind, sun, waves, tides, etc.) during their intensity and use it later to generate stable energy in fuel cells when the need arises. Hydrogen can be used for conversion of low-cost electric power in excess using water electrolysis in order to preserve it and then convert it back to ensure additional power during peak loads, i.e., a backup power source.

• Transport: Hydrogen fuel cell vehicles offer a zero-emission alternative to gasoline-powered cars, trucks and airplanes. Based on achievements of science and technology in the field of hydrogen fuel cells during the last decades, new prospects are opening up for the use of hydrogen as an energy carrier in transport and energy sector. Hydrogen is characterized by a high specific mass energy content. It contains three times more energy per unit mass than gasoline. Hydrogen can be used as a motor fuel in internal combustion engines (ICEs) of various vehicles with their minor modifications. Hydrogen is also characterized by high combustion rate and efficiency as well as good flammability in a mixture with air in a wide range of temperatures, thus ensuring quick engine starting at any ambient temperature.

• Industry: Hydrogen can be used in industrial heat production, steel making and various chemical processes, reducing carbon dioxide emissions and increasing process efficiency. Hydrogen is the most universal reagent for petroleum refining when removing sulfur compounds, nitrogen, oxygen, etc. Hydrogen is used at refineries in such processes as hydrocracking, desulfurization (hydrotreatment, hydroskimming), dearomatization, lube refining, etc.

The main advantages of using hydrogen are as follows:

High energy density: Hydrogen contains three times more energy per unit mass than gasoline, which makes it ideal for high-performance applications such as long-distance transportation and heavy machinery.

Clean combustion: Unlike fossil fuels, hydrogen burns cleanly, producing only water vapor, which makes it essential in fighting against climate change and air pollution.

Versatility: Hydrogen can be produced from various sources, including renewable resources such as solar, wind, and biomass, as well as fossil fuels using carbon capture and storage technology. Thanks to this, it is possible to adapt production to specific needs and environmental goals.

Diverse applications: Hydrogen's adaptability allows it to be used in a variety of industrial applications from fuel cells in electric vehicles to raw materials for chemical processes.

The main challenges associated with hydrogen utilization are as follows:

Storage and transportation. The low density of hydrogen at room temperature poses an issue in storage and transportation. Currently, research continues on developing such efficient methods as the use of compressed gas, liquid hydrogen and metal hydrides, etc.

Infrastructure development. Widespread deployment requires significant investments in the construction of hydrogen refueling stations, pipelines, and production facilities. Public-private partnerships and policy initiatives are crucial in this regard.

Cost competitiveness. At present, producing clean hydrogen can be more expensive than producing traditional fuels. Technological advances and economies of scale are key to reducing costs.

1.2 Hydrogen as a fuel for engines

Wide prospects are opening up for the use of hydrogen as a fuel, including in space engineering. To increase the flight range and duration of modern promising orbital, lunar and interplanetary spacecraft, it is necessary to improve the performance characteristics of hydrogen. First of all, it means reducing the volatility (losses) and increasing the density of hydrogen fuel, as well as accelerating the rate of chemical reactions. An effective way to resolve these issues is to use hydrogen in liquid form (in cryogenic state).

As rocket propellants, these products have been studied to a far unequal extent. Despite the difficulties related to its use, liquid hydrogen is most widely utilized in rocket engineering. Hydrogen was proposed as a rocket fuel by Russian scientist K. E. Tsiolkovsky in 1903. In the future, the scope of its application will expand.

In his theoretical works on cosmonautics, K. E. Tsiolkovsky, along with the presentation of the fundamental principles of jet propulsion, analyzed the possibilities of using various chemicals as rocket propellant components.

In his fundamental work, Exploration of the Universe with Rocket Propelled Vehicles, published in 1903, K. E. Tsiolkovsky recommended using liquid oxygen and hydrogen as a rocket propellant, while considering the propellant only in terms of obtaining the maximum gas velocity. No other use of these substances in rockets was envisioned, the “explosion tube” (combustion chamber) is cooled with liquid metal.

In his subsequent works, deepening and detailing the theory of jet propulsion, K. E. Tsiolkovsky simultaneously expanded his views on the possibility of using various chemical elements and compounds as rocket propellant components.

For many years, his attention was focused on selecting a fuel for its combustion with liquid oxygen. Using oxygen and hydrogen as a reference pair for calculations, K. E. Tsiolkovsky considered various substances suitable for use as propellants: primarily, various hydrocarbons such as crude oil, gasoline, benzene, ethylene, and turpentine.

In his work Space Rocket. Experimental Preparation, published in 1927, K. E. Tsiolkovsky allowed the use of an oxygen-containing compound — nitrogen anhydride — instead of pure oxygen. In the same work, he also was critical about the use of hydrogen: “Liquid hydrogen is not suitable for use at all, especially at first. Reasons: high cost, low temperature, heat of evaporation, complicated storage. It is more practical to use hydrocarbons with as much relative amount of hydrogen as possible.”

In 1932–1933, K. E. Tsiolkovsky wrote the Rocket Propellant paper (published in 1936), where he outlined the requirements for the rocket propellant component properties, and not only in terms of maximum energy efficiency but also in terms of performance. Analyzing various combinations of chemical elements and compounds, he came to the following conclusions: “Liquefied gases are generally unsuitable on account of their low temperature … Hydrogen is unsuitable on account of its low density and of the difficulty of storage in liquid form … Liquid oxygen represents a certain inconvenience on account of the storage difficulty …” Further followed a generalizing conclusion: “Hydrogen and oxygen in isolated form are also inconvenient, they are best replaced by weak compounds with other elements”. He also recommended using nitrogen compounds of oxygen instead of oxygen and hydrocarbon compounds instead of hydrogen.

Methane as a rocket fuel is currently intensively discussed, studied and applied. Significantly inferior to hydrogen in terms of specific impulse, it is superior to it in terms of density of fuel and propellants based on it. Another fuel used for comparison is high-boiling fuel RG-1 (hydrocarbon fuel for rocket engines, derived from petroleum refinery products, utilized in some Russian launch vehicles (LV) using liquid oxygen as oxidizer). Methane is superior to it in terms of specific impulse, but is far inferior to it in terms of density.

The comparison of these fuels in terms of ballistic characteristics depends to some extent on the energy scheme of the propulsion system and the ballistic scheme of the space carrier. The undoubted advantage of methane is the possibility of obtaining reducing generator gas and the convenience of turnaround servicing of the reusable propulsion system.

Liquefied natural gases represent the very same methane with other hydrocarbons. Their emergence as rocket fuels is driven by economic considerations. Their disadvantages (compared to methane) include a particular spread of energy parameters due to possible composition variation.

Liquid propane has not been considered to date as a rocket fuel. Being slightly inferior to methane in terms of specific impulse, it is superior to it in terms of density. Propane has a very wide temperature range of liquid state and, therefore, deep supercooling capabilities, which deserves energetic and ballistic elaboration.

Liquid ammonia was used as a fuel in experimental full-scale engines with fluorine and oxygen oxidizers. It is used as a working fluid in electric heating and electrothermal low-thrust rocket engines.

In design development, liquid diborane fuel is considered a component of energy-efficient propellant that can be stored for a long time in deep space conditions: OF2 + B2H6.

The energy characteristics of cryogenic propellants and thermophysical properties of combustion products in a wide range of compositions and parameters of liquid rocket engines are given in Ref. [1].

Table 2 shows the energy characteristics of cryogenic liquid rocket propellants (see Table 3).Table 1 Basic physical and chemical properties of cryogenic fuels.

Table 1Fuel	Chemical formula	Temperature of phase transition, °C	Critical parameters	Density of liquid at	ΔHf (298.15) of gas	Total enthalpy at Tboil,	
Tmelt	Tboil	Tcr, K	Pcr, MPa	Tboil	kJ kg−1	kJ kg−1	
Liquid hydrogen	H2	−259.33	−252.88	33.23	1.316	71.39	0	−4,407	
Liquid methane	CH4	−182.48	−161.49	190.55	4.641	422.0	−74.60	−5,554	
Liquid propane	C3H8	−187.65	−42.06	369.99	4.264	579.4	−104.5	−2,889	
Liquid ammonia	NH3	−77.72	−33.42	405.55	11.29	682.8	−45.94	−4,186	
Liquid diborane	B2H6	−164.85	−92.5			437	38.45	669	

Table 2 Energy characteristics of cryogenic liquid rocket propellants. Pp = 150 MPa.

Table 2Fuel	Oxidizer	ε	αopt	Κm
kg of oxid.
kg of fuel	ρf,
kg m−3	Tch, K	β,
m s−1	Jvs,	
m s−1	kg s kg−1	
Liquid hydrogen	O2(liq.)	300	0.65	5.159	333	3,385	2,372	4,383	447.0	
3,000	0.75	5.952	362	3,564	2,322	4,664	475.6	
F2(liq.)	300	0.70	13.194	624	4,850	2,518	4,637	472.8	
3,000	0.95	17.901	730	5,120	2,452	4,905	500.2	
Liquid methane	O2(liq.)	300	0.91	3.630	835	3,674	1,842	3,590	366.1	
3,000	0.96	3.830	844	3,676	1,825	3,900	3,97.7	
Liquid propane	O2(liq.)	300	0.87	1.157	926	3,769	1,816	3,546	361.6	
3,000	0.94	3.411	937	3,770	1,793	3,858	393.4	
Liquid ammonia	O2(liq.)	300	1.00	1.409	893	3,118	1,789	3,344	344.0	
3,000	1.00	1.409	893	3,118	1,789	3,563	363.3	
F2(liq.)	300	1.00	3.347	1,179	4,780	2,217	4,083	416.3	
3,000	1.00	3.347	1,179	4,788	2,217	4,302	438.7	
Liquid diborane	O2(liq.)	300	0.60	2.089	750	3,931	2,230	3,983	406.2	
3,000	0.57	1.976	741	3,860	1,833	4,367	445.4	
F2(liq.)	300	0.62	3.628	990	4,886	2,240	4,304	438.9	
3,000	0.74	4.330	1,038	5,027	2,254	4,672	476.4	
RG-1	O2 (liq.)	300	0.83	2.888	1,043	3,827	1,785	3,489	355.8	
3,000	0.93	3.159	1,049	3,827	1,757	3,802	387.7	

Table 3 Efficiency of hydrogen utilization.

Table 3Hydrogen consumers	Utilization efficiency	
Hydrogen-powered internal combustion engine	Wider ignition limits compared to conventional motor fuels. High thermal efficiency (hydrogen — 37.5 … 43 %, conventional motor fuel — up to 30 %). Using glow ignition instead of expensive spark ignition. Reduced oil consumption and engine wear, easy starting.	
Hydrogen fuel cells	Efficiency of fuel cells in generating electricity — up to 50 … 85 %. Development of hybrid units (fuel cell – gas turbine) with efficiency up to 70 %. Use of fuel cells in various means of transportation and development of electrochemical fuel cell generators.	
Hydrogen-fueled power plants	Use of hydrogen with oxygen as a fuel in steam generators increases efficiency up to 98.0 … 99.5 % due to the increase of specific heat power, decrease of the specific volume of the unit; reduces start-up duration; reduces transient process duration at load variation. Thermal efficiency for hydrogen-fueled GTUs reaches 60 % at maximum temperatures of 1500 … 2000 K. Reheating in turbines using hydrogen increases efficiency by 3 %.	
Thermal plants with a hydrogen atmosphere	Switching to an energy-saving heat-treatment furnace (steel annealing) with a hydrogen protective atmosphere can yield fuel savings of up to 63 %.	
Metallurgical plants using hydrogen as a reducing agent	Hydrogen is an effective reducing agent for metals in the high temperature region. In metallurgy, the efficiency of reduction with hydrogen is three times higher compared to CO. The processes of direct iron production represent a promising direction of hydrogen utilization, which will make it possible to stop using traditional energy-consuming methods in steel production.	

Hydrogen is an efficient fuel, which is increasingly used in rocket and aviation engineering, fuel power engineering. This is due to the fact that hydrogen, compared to traditional liquid hydrocarbon fuels, has a number of significant energy and environmental advantages.

For the production of hydrogen, inexhaustible raw materials (water) are used. Besides, its combustion products do not contain toxic or air-polluting substances, which are formed in significant quantities, for example, during combustion of hydrocarbon fuels. Hydrogen is characterized by low boiling point and low density, wide ignition concentration limits and low ignition energy; non-knocking combustion of a hydrogen mixture can change to knocking combustion. Hydrogen is also characterized by high fire and explosion hazard. Therefore, when handling hydrogen, it is necessary to be well aware of its thermophysical, chemical and operational properties, provide for organizational and technical measures to ensure fire and explosion safety of facilities and products, design and use special means for storage, transportation and refueling.

In recent years, significant progress has been made in the area of using hydrogen technologies in power engineering, transportation, various industries as well as other spheres of human life [2,[3], [4], [5], [6]]. Hydrogen technologies are of great importance for rocket and space engineering. Oxygen-hydrogen propellant has been used in LVs and space tugs for more than 40 years. One of the consistent trends in the development of rocket and space engineering is an increase in the performance of launch vehicles, which can be ensured based on the use of highly efficient oxygen-hydrogen propellant components. Such components are used in the USA (in the Centaur-3 upper stage for Atlas-5 LV, in the Centaur first stage and space tug for Delta-4 LV), in the ESA (in the first and second stages of Ariane-5 ESA LV; ESC-B space tug is being developed for the prospective Ariane-5 ESB LV), in Japan (in both stages of the modified H-2A LV family), in China (in the upper stages of CZ-3, -3A, -3B LVs, as part of the first and second stages of the new-generation CZ-5 LVs), in India (as part of the third stage GS3 of the GSLV LV). Besides, in recent years, issues of transition to environmentally friendly rocket propellant components are becoming more acute. All this increases the relevance of work on developing LV space tugs and stages using oxygen-hydrogen propellant. Over the last years, the organizations of the Federal Space Agency Roscosmos (Russia) developed significant scientific-and-technical, technological and production capacities, which made it possible to design and test-fly a unique Energia-Buran system using highly efficient oxygen + hydrogen propellant components. At the same time, oxygen-hydrogen engines with specific indicators at the level of world achievements were developed, including: liquid rocket engines (LREs) 11D56 (Design Bureau of Chemical Machine Building), 11D57 (Lyulka Experimental Design Bureau), LRE 11D122 (Design Bureau of Chemical Automation), and nuclear rocket engine 11B91 (Design Bureau of Chemical Automation).

As part of a joint Russian-Indian project, Khrunichev State Research and Production Space Center developed a third stage for the GSLV LV using oxygen + hydrogen propellant components. Flight tests and the first operational launch of this LV were already successfully conducted. Currently, Russia does not operate LVs and space tugs using oxygen-hydrogen components but has a significant reserve of oxygen-hydrogen LREs. The main areas of work in the development of oxygen-hydrogen space tugs and LV stages include:— development of advanced technological and design solutions for heavy-lift LVs and space tugs, ensuring high level of design excellence, reliability, safety, and application efficiency;

— improvement and development of the test bench and experimental facilities, re-equipment of production, and training of scientific and technical personnel;

— restoration, modernization of production for the development of new domestic oxygen-hydrogen LREs;

— comprehensive system-and-technological as well as design-and-engineering substantiation for a reusable rocket-space system (RRSS) option, ensuring development of the first stage reusable system with acceptable performance, reliability and application safety indicators.

Works on determining the appearance and main characteristics of transport modules using solar thermal and electric propulsion systems (PSs) are quite significant. Along with solving problems of long-term liquid hydrogen storage in space, issues of control, degradation of solar battery elements, etc., the possibility of developing (based on such PSs) universal transport and energy platforms for new-generation spacecraft, ensuring inter-orbital transfers and subsequent power supply and spacecraft control in orbit, is of particular interest. Oxygen-hydrogen sources of electrical energy are characterized by the highest (compared to other electrochemical groups) theoretical specific energy, which determines the increased interest in the use of hydrogen-oxygen electrochemical generators in rocket and space engineering. Power units based on hydrogen-oxygen electrochemical generators as a basis for power supply of manned reusable spacecraft seem quite promising.

The Russian Federal Space Agency Roscosmos considers the use of hydrogen in rocket and space engineering one of the promising areas of scientific and technical activity.

Currently, hydrogen and hydrogen-based products (e.g., ammonia) are being effectively used in particular branches of technology (e.g., ammonia is used in engines as a propellant in pure form or when mixed with hydrogen).

Global decarbonization requires the increased use of zero-carbon fuels. Compared to hydrogen, ammonia is easier to store, transport, and produce. In addition, products of complete combustion of ammonia are water and nitrogen. Therefore, ammonia is an ideal green fuel for internal combustion engines. Drawbacks relate to the high ignition energy and low laminar flame speed of ammonia. A three-dimensional numerical study investigated the potential of converting existing diesel engines to ammonia spark ignition operation [7]. The results indicated a slower kernel inception process, but the speed of the fully developed turbulent flame was enough to complete the bulk combustion process despite the lower laminar flame speed. The problem with pure ammonia operation was the reduced combustion efficiency and the high level of unburned ammonia emissions since the slow spark inception process can be compensated by a larger compression ratio. The results also suggested that emissions formation and subsequent oxidation were a more complex phenomenon.

Under the paradigm of carbon neutrality, ammonia-hydrogen (NH3–H2) blended fuel presents itself as a zero-carbon alternative to petroleum-based fuels, effectively reducing carbon emissions originating from internal combustion engines [8]. In the combustion process of conventional hydrocarbon fuels, the production of nitrogen oxides (NOX) predominantly arises from nitrogen present in the atmosphere, which occurs through the Zeldovich mechanism under high-temperature conditions. These NOX species, commonly referred to as thermal NOX, rely on inert nitrogen. However, the utilization of ammonia fuel activates the reactivity of nitrogen element, leading to the nitrogen-containing species formation, including NOX, termed as fuel NOX. Consequently, the combustion of ammonia-hydrogen fuel entails the coupling of thermally formed nitrogen oxides and fuel-derived nitrogen oxides.

In pursuit of carbon neutrality, zero-carbon ammonia fuel emerges as a viable solution for reducing energy carbon emissions. Integrating ammonia into diesel engines, by partially substituting it for diesel, presents a recognized method for mitigating carbon emissions. However, introducing ammonia as a fuel adds an alternative source of elemental nitrogen, in addition to air, thereby increasing the formation pathways for nitrogen-based pollutants and altering emission characteristics compared to traditional engines. To enhance understanding of these emission characteristics within the ammonia-diesel dual-fuel system, on the studies [9] employed a validated three-dimensional (3D) computational fluid dynamics (CFD) model to meticulously analyze the formation and evolution of in-cylinder nitrogen-based pollutants.

In pursuit of carbon neutrality, the adoption of zero-carbon fuels in internal combustion engines offers a path to zero carbon emissions. Among such fuels, ammonia (NH3) stands out as an effective hydrogen energy carrier with a higher energy density and a more advanced production-storage-transportation lifecycle than hydrogen (H2) fuel, making it a superior alternative [10]. Nevertheless, achieving high combustion efficiencies in engine cylinders requires the use of fuels with fast flame speeds, since the time scales of the combustion event are practically milliseconds. The inherent flame speed of NH3 falls short, typically necessitating augmentation with H2.

The increasing trend towards global carbon neutrality is driving interest in ammonia fuel as a potential zero-carbon solution for transportation. However, due to the non-ideal combustion characteristics of ammonia, it is necessary to mix it with hydrogen to achieve better engine performance. While generating hydrogen from ammonia on-board is a key technology, there has been limited research in this area, which is hindering the introduction of ammonia engines to the market. Paper [11] proposed an initial study on the feasibility of thermochemical fuel reforming (TFR) technology for generating hydrogen from ammonia fuel-rich operations. A zero-dimensional engine model, validated against experimental results, was used to assess the potential of the TFR approach and identify any barriers to implementation. The results indicated that the optimum air-fuel ratio for hydrogen generation is an equivalence ratio of two, as it maximizes hydrogen production rates while minimizing operational complexities.

Paper [12] experimentally examined an ammonia-diesel dual fuel system, not widely covered in existing literature but acknowledged as an effective approach to reduce engine carbon footprints in alignment with global decarbonization trends, focusing on enhancing understanding of performance, combustion, and emission characteristics vital for designing and optimizing these engines for commercialization. The results indicated that in an ammonia-air mixture atmosphere, diesel undergoes a prolonged ignition process, enhancing the role of premixed combustion. Increasing ammonia substitution at constant speed and load reduces the weight of mixing-controlled combustion, leading to larger areas in the chamber where diesel flames cannot reach. Ammonia oxidation mainly occurs near the diesel flame, as overly lean ammonia-air mixtures fail to sustain stable flame propagation. This results in considerable unburned ammonia emissions, particularly in regions beyond diesel flame reach and engine crevices, adversely affecting combustion efficiency and diminishing the thermal efficiency advantages of such operation.

1.3 Safety of hydrogen use

Safety measures for handling, storage and transportation of hydrogen are presented in the following regulatory documents:

- in international standards:

ISO 13984: Liquid Hydrogen — Land Vehicle Fueling System Interface.

ISO 14687: Hydrogen Fuel — Product Specification.

ISO/CD 13985: Liquid Hydrogen — Land Vehicle Fuel Tanks.

ISO/WD 13986: Tank Containers for Multimodal Transportation of Liquid Hydrogen.

ISO/WD 15594: Airport Hydrogen Fueling Facility.

ISO/WD 15866: Gaseous Hydrogen Blends and Hydrogen Fuel — Service Stations.

ISO/WD 15869: Gaseous Hydrogen and Hydrogen Blends — Land Vehicle Fuel Tanks.

ISO/WD 15916: Basic Requirements for the Safety of Hydrogen Systems.

ISO/AWI 17268: Gaseous Hydrogen — Land Vehicle Fueling Connectors.

ISO/TR 15916: 2004(E): Basic Considerations for the Safety of Hydrogen Systems.

NFPA 50A: Standard for Gaseous Hydrogen Systems at Consumer Sites.

- in the international standards of the European Association of Industrial Gases:

IGC 06/02/E: Safety in Storage, Handling and Distribution of Liquid Hydrogen.

IGC 100/03/E: Hydrogen Cylinders and Transport Vessels.

IGC 122/04/E: Environmental Impacts of Hydrogen Plants IGC 121/04/E: Hydrogen Transportation Pipelines.

In the practical solution of specific problems related to the use of hydrogen, it is necessary to carefully follow the safety rules. Hydrogen safety covers the safe production, handling and use of hydrogen, particularly hydrogen gas fuel and liquid hydrogen. Hydrogen possesses the NFPA 704's highest rating of four on the flammability scale because it is flammable when mixed even in small amounts with ordinary air. Ignition can occur at a volumetric ratio of hydrogen to air as low as 4 % due to the oxygen in the air and the simplicity and chemical properties of the reaction.

Of all the various hazards associated with hydrogen handling, the most dangerous is its uncontrolled ignition. Mixtures of hydrogen and oxidizers are flammable in a wide range of concentrations (from 4 to 75 vol% in air), temperatures and pressures, while mixtures of stoichiometric composition (approx. 30 %) are especially flammable, which determines their high hazard in confined spaces.

In most cases, hydrogen combustion in a confined space leads to deflagration — an explosive mode characterized by turbulent propagation of the flame at a high rate, less than the speed of sound in the environment not covered by combustion, and a significant increase in pressure after combustion compared to the initial pressure (for a stoichiometric mixture). Under certain conditions, deflagration transfers to the most dangerous explosive mode — detonation.

Special operating materials contacting with hydrogen must be used. For metallic materials, especially ferritic steels when stressed, contact with hydrogen is quite dangerous in terms of reduction of the strength properties due to embrittlement, as well as hydrogen corrosion, to which mainly low-alloyed steels are exposed at high temperatures, which can destruct tanks and other equipment. An important consequence of the extremely low boiling point of liquid hydrogen (20.3 K) is the following: when interacting with it, all gases except helium condense and solidify, becoming a potential source of valve blocking and pipe clogging. Gaseous hydrogen can be compressed to very high pressures, but the release of the energy accumulated during compression generates an explosive wave. Rapid “thawing” (phase transition) of liquid hydrogen in a confined space (tank or pipe) can have similar consequences.

In normal state, hydrogen is not dangerous to the human body, but at high concentrations in a room it causes suffocation, like natural gas (methane), due to displacement of air. In liquid state, hydrogen can cause severe frostbite, which also does not set it apart from other liquefied gases.

1.3.1 General safety requirements

- avoiding dangerous vicinity of devices and systems for hydrogen production, storage, transportation and use to areas where oxidizing and easily flammable substances, spark-hazardous equipment can be potentially available.

- when designing, manufacturing, storing, transporting, installing, adjusting hydrogen devices and systems, the main safety requirement is to ensure tightness to avoid possible hydrogen leakage or ingress of oxidizers into their internal cavities with hydrogen.

- to improve the safety of a hydrogen system, it is important to consider significant risks associated with pipes and fittings in its design and construction. If possible, open laying of hydrogen pipelines indoors should be performed. If it is necessary to lay those pipelines in channels together with other pipelines (which requires justification in the design documentation), certain conditions must be observed:

- for various purging operations (pumping and filling, pressurizing and removing, straight-forward flow), an inert gas unit is required, protected against mixing with hydrogen. Hydrogen devices should be purged with inert gas before hydrogen supply and after its removal, blowing the air out of the system before hydrogen supply, and blowing the hydrogen out of the system before air entry.

- the common method of hydrogen disposal is to release it into the atmosphere through a vent (with no hydrogen combustion) or burn it in a flare system (hydrogen is ignited at the point of release and burns up).

- the ventilation system must be equipped with devices for fire extinguishing as well as purging the air or hydrogen contained in it.

- areas of possible hydrogen emission at production premises shall be equipped with various sensors: hydrogen detectors, hydrogen combustion detectors, and a sound and light alarm system.

- hydrogen devices and systems shall be equipped with automatic fire-fighting equipment.

- during operation, hydrogen devices and systems shall be periodically inspected for tightness to detect and eliminate possible leaks.

- there are special requirements for the safety of certain types of hydrogen devices and systems, especially for the safety of the most popular types of equipment designed for the production of commercial hydrogen (electrolyzers and compressors), its storage and transportation (liquid hydrogen storage and transportation facilities, gas holders, high-pressure cylinders, on-board storage systems), as well as its use as an energy carrier (electrochemical generators).

Organizations using hydrogen shall develop internal regulatory safety documents, train all categories of personnel and educate employees to give the absolute priority to the requirements set in these documents and be intolerant to any evasion or deviation from their unconditional fulfillment, as well as monitor compliance with these requirements.

1.4 Energy efficiency of hydrogen production and consumption

The choice of hydrogen as an energy source is due to a number of advantages, the main of which are environmental cleanliness and high energy level per unit mass. Based on forecasts, global consumption of hydrogen in the next century may increase 16 times from 50 to 800 million tons, with the bulk of it being used in energy and transport sectors. For transition to hydrogen energy (commercialization), it is necessary to solve the issues of production of cheap enough hydrogen in large quantities, its storage, transportation and efficient use.

Let's consider the energy costs of hydrogen at different commercialization stages: production, storage, and transportation. When the energy costs of production are analyzed, it is taken into account that the production of hydrogen by natural gas conversion and water electrolysis is the target. Hydrogen from oil and coal is usually a by-product of the refining process, by-product coke industry, etc. Currently, hydrogen is globally produced from natural gas (85 %), oil (7 %), coal (4 %), and from water by electrolysis (4 %). Specific energy consumption per 1 m3 of H2 obtained by electrolysis consists of 4.5 … 5.1 kW h of power and 0.92 … 1.1 kg of water. Specific energy consumption for hydrogen production from natural gas consists of 0.43 … 0.66 m3 of natural gas, 0.038 … 0.07 kW h of power, and 0.9 … 1.7 kg of water.

When the energy costs of hydrogen storage are analyzed, it is taken into account that the most common storage methods are in compressed gaseous as well as in liquid or liquefied forms. Specific energy consumption for storage of 1 m3 of hydrogen in gaseous form amounts to 0.04 … 0.08 kW h, and in liquefied form — to 0.95 … 1.34 kW h. There are also other methods to store hydrogen: in hydrates, by cryogenic adsorption, or using carbon nanostructures.

When hydrogen transportation is analyzed, it is taken into account that mainly gaseous (by pipelines) or liquefied (by road and rail) hydrogen is currently transported. Each transportation option has its own range of applications. For instance, in case of a hydrogen flow rate of more than 10 t/h for distances up to 1,000 km, pipelines are used, at lower flow rates and closer distances, liquefied hydrogen tanks are used.

The main energy costs of hydrogen commercialization are the costs of its production, including energy costs of 398 … 451 % of the energy of hydrogen produced by electrolysis and 154 … 233 % of the energy of hydrogen produced by steam conversion of natural gas. The costs of hydrogen storage are 10 … 16 % of the energy of hydrogen produced for gaseous storage and 90 … 127 % of the energy of hydrogen produced for liquefied storage.

The costs of hydrogen transportation per 1,000 km are 3–30 % of the energy of hydrogen to be transported by pipes and 31 % and 7 % of the energy of hydrogen to be transported by road and rail, respectively.

Thus, the current methods of hydrogen commercialization are unprofitable in terms of energy, but it is possible to ensure energy profitability of gas by finding ways to produce energy-saving hydrogen that would be quite cheap in terms of energy.

Among the considered methods, steam conversion of natural gas is characterized by the lowest energy costs of hydrogen production, which amount to 154 … 233 % of hydrogen energy. The costs of electrolysis amount to 398 … 451 % of the energy of produced hydrogen, but this method of production is quite promising with the use of advanced systems of renewable energy sources, development of nuclear-hydrogen power engineering, or hydrogen production at thermal power plants with improvement of their energy efficiency. In addition to energy-consuming hydrogen production systems, energy-saving methods have been proposed where hydrogen production is accompanied by additional energy-saving effects. The essence of the method is that hydrogen is produced based on the comprehensive utilization of natural gas at iron works with achievement of significant energy-saving effects.

The energy costs of hydrogen production can be justified if it is used efficiently since the use of hydrogen can have an effect exceeding the costs of its production. Table 1 shows consumers, the efficiency of which is improved due to the use of hydrogen. The energy efficiency of hydrogen utilization can be assessed by comparing the energy costs of its production and the energy savings resulting from its use. The energy efficiency coefficient can serve as a quantitative characteristic in this case. The lack of energy profitability in hydrogen production can be offset by energy-efficient hydrogen utilization.

The analysis of energy efficiency of the current target methods of production, storage, and transportation shows that the costs of hydrogen commercialization are 154 … 614 % of its energy, which corresponds to the energy efficiency coefficient of 0.651 … 0.163. In addition to energy-consuming methods of hydrogen production, it is possible to use energy-saving methods based on achieving energy-saving effects when combined at iron works and refineries. Energy-efficient use of hydrogen based on the energy efficiency coefficient shows that the energy-saving effects of hydrogen utilization are 4.73 times higher than the energy costs of hydrogen production.

1.5 Hydrogen isotopes and their applications

Hydrogen occurs in three natural isotopic forms: protium — light hydrogen, heavy deuterium, and superheavy tritium. All of them can be found in their natural state. In addition to those listed, there are four artificially synthesized isotopes: quadium, pentium, hexium, and septium. These varieties are characterized by extreme instability, the lifetime of their nuclei is 10−22–10−23 s. Thus, in total, seven isotopic varieties of hydrogen are currently known.

Light hydrogen. Light hydrogen has the simplest atom. Protium, with an atomic mass of 1.0078 amu, has a nucleus that contains only one particle, the proton. Since it is stable (in theory, the lifetime of a proton is estimated to be no less than 2.9 × 10−29 years), the protium atom is also stable. In writing nuclear reactions, it is denoted as 1H1, or simply p (“proton”). The light isotope makes up almost 99.99 % of all hydrogen; only a little more than one hundredth of a percent is accounted for by other forms.

In molecular form, hydrogen enters into chemical interactions at high temperatures since it takes a lot of energy to break down its fairly strong molecule. Atomic hydrogen is characterized by very high chemical activity.

Deuterium. The heavy isotope of hydrogen, deuterium, has a nucleus consisting of a proton and a neutron. The atomic mass of deuterium is twice as large — 2.0141. Accepted designation: 2H1 or D. This isotopic form is also stable since during the processes of strong interaction in the nucleus, the proton and neutron are constantly transforming into each other, and the latter does not have time to undergo decay. On Earth, hydrogen contains 0.011 … 0.016 % deuterium. Its concentration varies depending on the environment: in seawater, it is more abundant, and as part of, for example, natural gas, it is significantly less. Deuterium melts at 18.6 K (light hydrogen — at 14 K) and boils at 23.6 K (protium — at 20.3 K). In general, heavy hydrogen shows the same chemical properties as protium, forming all types of compounds typical for this element, but it also has some peculiarities related to the significant difference in atomic mass — after all, deuterium is two times heavier. It should be noted that for this reason the isotopic forms of hydrogen have the greatest chemical differences of all the elements. In general, deuterium is characterized by lower (5–10 times) reaction rates.

Role of deuterium in nature. Heavy hydrogen nuclei take part in the intermediate stages of the thermonuclear cycle. The Sun shines thanks to this process, at one stage of which the hydrogen isotope deuterium, merging with a proton, forms helium-3.

Water that contains one deuterium atom in addition to protium is called semi-heavy water and has the following formula: HDO. In the D2O heavy water molecule, deuterium completely replaces light hydrogen. Heavy water is characterized by slow chemical reactions.

One of the methods to obtain deuterium is to obtain it as part of water. There are several ways to enrich water with deuterium. Rectification is the process of separating mixtures into components boiling at different temperatures. This separation can be achieved through repeated evaporation and condensation of the isotope mixture in liquid hydrogen in rectification columns. Another method is electrolytic separation. This method is based on the fact that, during water electrolysis, a light isotope more actively detaches from its molecules. Electrolysis is carried out in several steps. Another method is ion-isotopic exchange where mutual substitution of ions of different isotopes as part of reactants occurs. Currently, this method using water and hydrogen sulfide as reacting components is the most effective and cost-efficient.

Tritium. Superheavy isotope of hydrogen, which has a proton and two neutrons in its nucleus. Its atomic mass is 3.016, which is approximately three times that of protium. Tritium is denoted by T or 3H1. It melts and boils at even higher temperatures: 20.6 K and 25 K, respectively. It is a radioactive unstable isotope with a half-life of 12.32 years. It is formed when the nuclei of atmospheric gases, such as nitrogen, are bombarded by cosmic ray particles. The decay of the isotope occurs with the emission of an electron (beta decay), with one neutron in the nucleus being transformed into a proton, and the chemical element increases its atomic number by one unit, becoming helium-3. In nature, tritium is present only in trace amounts. Superheavy hydrogen is formed in heavy-water nuclear reactors when deuterium captures slow (thermal) neutrons. Some of it is available for extraction and serves as a source of tritium. It can also be obtained as a decay product of lithium when the latter is irradiated with thermal neutrons. Tritium is characterized by low decay energy.

Applications of hydrogen isotopes. Light hydrogen is used in many industries: in the chemical industry (to produce ammonia, methanol, hydrochloric acid, and other substances), in oil refining and metallurgy (to reduce refractory metals from oxides). It is also used at some stages of the production cycle (in the production of solid fats) in the food and cosmetics industry. Hydrogen serves as a rocket fuel and is used in laboratories in science and manufacturing. Deuterium is indispensable in the nuclear power industry as a neutron moderator. It is also used as a coolant in heavy water reactors allowing the use of natural uranium, which reduces enrichment costs. Besides, along with tritium, it serves as a component of the working mixture in thermonuclear weapons.

The chemical properties of heavy hydrogen allow it to be used in the production of medicines in order to slow down their removal from the human body. Finally, deuterium (as well as tritium) is quite promising as a fuel in the thermal nuclear power industry. Unfortunately, we have not found any works that would summarize the properties of deuterium and tritium.

1.6 Conclusion

The existing operational challenges and disadvantages of hydrogen can be technically overcome, and numerous technical solutions have already been proposed. Despite the existing challenges, ongoing research, infrastructure development, and collaboration between industries and governments are accelerating the hydrogen revolution. By utilizing the unique properties of hydrogen, it is possible to create a cleaner and more sustainable future based on this versatile element.

The use of hydrogen in various industries is still in its early stages, but the possibilities are huge. As technology advances and infrastructure expands, hydrogen can become a key player in a cleaner and more sustainable future. By studying its properties and characteristics, optimizing production methods, and overcoming existing challenges, we can unlock the true potential of this versatile element and revolutionize industries in all fields. Hydrogen's potential to transform industry is undeniable, but a better understanding of its properties, challenges and specific applications across various sectors is crucial. However, despite the long studies of hydrogen properties, for most fields, there are currently no reliable generalized data on the physical and chemical properties and thermodynamic characteristics of hydrogen. Some properties of hydrogen presented in the paper, and especially the dependence of its properties on temperature, are not available in the literature. The paper clarifies and summarizes data on the properties and thermodynamic characteristics of hydrogen.

2 State and composition

Hydrogen is a chemical element of group VII of the periodic table: atomic weight — 1.0079, molecular weight — 2.0158. A hydrogen molecule (dihydrogen) consists of two atoms joined by a covalent bond. Under normal conditions, hydrogen is a colorless, tasteless, odorless gas. In the liquid and solid state, it represents a colorless liquid or crystals, respectively.

There are three isotopes of hydrogen: protium, deuterium, and tritium with mass numbers 1, 2, and 3, respectively. The main component of natural hydrogen (99.984 %) is protium, the rest (0.016 %) is deuterium, while the tritium content is negligible (4⋅10−15 of the total number of atoms) [13].

Hydrogen consists of a mixture of two allotropic forms: orthohydrogen (o-H2) and parahydrogen (р-Н2) [14,15]. Both modifications are similar in chemical properties and differ in physical properties. Ortho-para hydrogen composition depends on temperature (see the calculated data in Table 4) and very slightly — on pressure [16,17]. The composition consisting of 25 % р-Н2 and 75 % о-Н2 is commonly referred to as normal hydrogen (n-H2), or simply hydrogen.Table 4 Ortho-para hydrogen composition depending on temperature [16].

Table 4T, K	Content
р-Н2, %	T, K	Content
р-Н2, %	T, K	Content
р-Н2, %	T, K	Content
р-Н2, %	
10.00	99.9999	40	88.727	90	42.882	250	25.264	
20.00	99.8210	50	77.054	100	38.620	300	25.072	
20.39	99.7890	60	65.569	120	32.959	350	25.019	
30.00	97.0210	70	55.991	150	28.603	400	25.005	
33.10	95.0340	80	48.537	200	25.974	500	25.000	
Note: The calculated values of ortho-para composition depending on temperature differ from the experimental data within the range of ±1 %, which does not exceed the experimental error.

The rate of spontaneous ortho-para conversion is proportional to the square of the concentration of hydrogen ortho modification, and the fraction of orthohydrogen is related to the conversion time by the following dependence [18]:(1) Χ=(1/Χ0+K⋅τ)−1,

where Х0 is the initial concentration of orthohydrogen, τ is the conversion time.

For liquid orthohydrogen, K = 3.17 ⋅ 106 s−1 (11.4 ⋅ 10−3 h−1).

3 Energy efficiency

Table 5 shows energy efficiency of the propellant О2(liq) + Н2(liq) depending on the ratio of components (Km) at corresponding boiling points. The calculations were performed using the thermal data given in the paper.Table 5 Energy efficiency of the propellant О2(liq.) + Н2(liq.) depending on the ratio of components (Km) at corresponding boiling points.

Table 5αox	Кm	ρf,
kg m−3	T, K	β,
m s−1	ε	Fα‾	Jvs	
m s−1	kg s kg−1	
0.85	6.746	389.1	3,666	2,266	300	30.6	4,337.5	442.3	
3,000	180.6	4,656.1	474.8	
5,000	267.4	4,706.8	480.0	
0.80	6.630	375.7	3,624	2,295	300	29.5	4,355.9	444.2	
3,000	171.4	4,662.2	475.4	
5,000	252.8	4,710.5	480.3	
0.75	5.953	361.8	3,563	2,322	300	28.4	4,369.8	445.6	
3,000	162.8	4,664.0	475.6	
5,000	239.1	4,709.9	480.3	
0.70	5.556	347.5	3,484	2,349	300	27.4	4,378.9	446.5	
3,000	154.4	4,661.1	475.3	
5,000	225.8	4,704.7	479.8	
0.65	5.159	332.6	3,384	2,374	300	26.4	4,383.2	477.0	
3,000	146.2	4,653.5	474.5	
5,000	213.2	4,694.4	478.7	
0.60	4.762	317.1	3,264	2,395	300	25.4	4,382.2	446.9	
3,000	138.4	4,640.0	473.2	
5,000	201.2	4,678.7	4,77.1	

4 Physical and chemical as well as operational properties

4.1 Thermophysical properties

4.1.1 Equation of state

The following equation of state is valid for hydrogen [19,20]:(2) PV = RT [1 + В(Т)/V+ С (Т)/V2].

The values of the B(T) coefficients for normal hydrogen (n–Н2) were obtained in the temperature range of 14–70 K, and, to determine them, the following equation can be used:(3) B(Т) = (151.9 ± 1.1)⋅10−6 (20.4/Т)1.37, m3⋅mol−1

The difference in the B(Т) value for n–Н2 and р–Н2 is equal to (1.6 ± 0.1)⋅10−6 m3 ⋅mol−1 and (2.0 ± 0.4)⋅10−6 m3 ⋅mol−1 for temperatures of 20.5 and 18.3 К, respectively [19]. The B(T) and C(T) coefficients for the considered temperature range from 24 to 100 K differ insignificantly in most cases for ortho- and parahydrogen and are given in Table 6. The values of the B(T) and C(T) coefficients can also be determined based on the following equations [20].(4) В = В0 (1 – Х5/4),

where Х = Т0/Т (Т0 = 109.83 K), В = 19.866⋅10−6 m3 mol−1 or В0 = ,Table 6 Coefficients В(Т), m3. mol−1, and С(Т), m6 ⋅ mol−2, in the range of temperatures of 16–423.15 K.

Table 6T,
K	В⋅10−6	С⋅10−12	T,
K	В⋅10−6	С⋅10−12	T,
K	В⋅10−6	С⋅10−12	
16	−204.2	–	38	−54.99	1,290	100.00	−2.52	609	
18	−172.9	–	39	−52.60	1,252	103.15	−1.69	580	
20	−148.8	–	40	−50.32	1,209	113.15	0.67	540	
22	−129.7	–	42	−46.19	1,144	123.125	2.63	560	
24	−112.8	1,207	44	−42.50	1,092	138.15	5.01	540	
25	−106.2	1,402	46	−39.18	1,046	153.15	6.89	522	
26	−100.3	1,580	48	−36.17	1,005	173.15	8.84	500	
27	−94.8	1,627	50	−33.39	964	198.15	10.65	458	
28	−89.66	1,612	55	−27.48	889	223.15	11.98	437	
29	−85.03	1,615	60	−22.70	838	248.15	12.97	415	
30	−80.73	1,600	65	−18.64	785	273.15	13.76	404	
31	−76.75	1,585	70	−15.22	743	298.15	14.38	370	
32	−72.99	1,550	75	−12.48	726	323.15	14.87	340	
34	−66.22	1,426	85	−7.63	659	373.15	15.60	303	
35	−63.17	1,426	90	−5.66	636	398.15	15.86	310	
35	−63.17	1,426	90	−5.66	636	398.15	15.86	310	
36	−60.26	1,377	95	−3.99	624	423.15	16.08	302	
37	−57.54	1,331	98.15	−3.06	530				

where Х = Т0/Т (Т0 = 109.781 K), В1 = 42.464, В2 = −37.1172, В3 = 2.2982, В4 = −3.0484(5) С = С0 ⋅Х1/2 (1 + С⋅Х3) [1 − exp (1 – X3)],

where Х = Т0/Т (Т0 = 20.615 K), С0 = 1.3105⋅10 −8 m6 mol−2, С = 2.1486.

The average deviations of the B(T) values, obtained from Eqs. (3), (4), from the experimental data, respectively, are as follows: ±0.13.10−6 m3 mol−1 and ±0.07 10−6 m3 mol−1, and for the C(T) values determined by Eq. (5): ±1.74⋅10−11 m6 mol−2. A number of empirical equations of state were derived for liquid and gaseous hydrogen. One of the simplest equations for parahydrogen has the following form [21].(6) P=−aV−m[1−(Vo/V)n]+RTV−b0+(c/V),

where а = 1.267⋅104 MPa; Vo = 23.48⋅106 m3 mol−1; m = 1.86; n = 6; b0 = 26.9⋅10−6 m3 mol−1;с = 2.375⋅10−10 m6 mol−2. The error of estimate is ±2 %.

In case of normal liquid hydrogen, the equation of state has the following form:(7) P = ao + a1 / V + a2 / V2 + a3 / V3 + (bo + b1 / V) T,

where Р — pressure, kg. cm−2, V — specific volume, cm3. g−1; ао = − 348.93; а1 = 28968.3;

a2 = −749,142; a3 = 5,298,480; b0 = −7.43; b1 = 224. The maximum discrepancy between the calculated and experimental data does not exceed ±0.5 %.

4.1.2 Melting point

The melting point of normal hydrogen at 0.1 MPa is minus 13.947 K, parahydrogen — minus 13.803 K [22]. Table 7 shows the calculated melting point values.Table 7 Melting point of normal hydrogen and parahydrogen [23].

Table 7Tmelt, К	P, MPa	Tmelt, К	P, MPa	Tmelt, К	P, MPa	
p-Н2	n-Н2	p-Н2	n-Н2	p-Н2	n-Н2	
13.810a	0.00703	–	20	22.71	22.18	50	221.5	220.7	
13.947a	0.4696	0.0073a	22	31.63	31.09	55	–	261.6	
14.0	0.5974	0.1699	24	41.26	40.68	60	–	307.9	
15.0	3.7640	3.3240	26	51.54	50.94	70	–	409.2	
16.0	7.1120	6.647	30	74.00	73.35	80	–	521.3	
17.0	10.7100	10.220	35	105.4	104.8	90	–	644.2	
18.0	14.51	14.01	40	140.5	139.8	100	–	777.4	
19.0	18.51	18.01	45	179.3	178.5	130	–	1,236.0	
						160	–	1,778.5	
a Triple point.

The data from Table 7 differ from the experimental data by no more than ±2.5 %, and from the data of other researchers — also by no more than ±2.5 % [[24], [25], [26]]. Based on the experimental data, an analytical relationship linking pressure and melting point for n-Н2 and р-Н2 in the pressure range from 0 to 539 MPa was proposed [27].(8) Р – Рtp/Тmelt – Тtp = А exp (–α/Тmelt) + В Тmelt,

where: А = 3,073 kPa⋅К−1; Тtp and Рtp — temperature and pressure at the triple point; α = 5.693 K;В = 67.55 kPa. К−2

The calculated data based on the equation differ from the measurement results by no more than ±2 %.

The dependence of the melting point of normal hydrogen on pressure in the pressure range from 400 to 1,900 MPa can be described by the following equation [28,29]:(9) Рmelt = −0.2442 .102 + 2.856.10−1 ⋅

The root-mean-square deviation of the calculated data from the experimental data is ±1.4 % in the pressure range from 0.1 to 1,860 MPa and temperature range from 50 to 160 K.

4.1.3 Boiling point

The boiling point of normal hydrogen is 20.384 K [30], of parahydrogen — 20.268 K [31]. The error of estimate for the Tmelt value has not been evaluated.

4.1.4 Critical parameters

Table 8 shows critical parameters for normal hydrogen and parahydrogen.Table 8 Critical parameters for normal hydrogen and parahydrogen.

Table 8Indicators	n-Н2 [17]	р-Н2 [1]	
Temperature, K	33.240	32.76 ± 0.015	
Pressure, MPa	1.2980	1.2759	
Density, kg⋅ m−3	30.12	31.43	

The data error has not been estimated. The differences between the data of a number of researchers do not exceed ±2.5 % for temperature and ±1 % for pressure.

4.1.5 Saturated vapor pressure

The saturated vapor pressure of normal hydrogen (experimental data) is given in Table 9 [30], and that of parahydrogen is given in Table 10 [31].Table 9 Saturated vapor pressure of normal hydrogen Рs, MPa [30].

Table 9T, K	Рs	T, K	Рs	T, K	Рs	T, K	Рs	
13.957	0.0072	20.0*	0.0901	24.93*	0.3158	29.207	0.7082*	
14.0	0.0074	20.39	0.1013	25.21*	0.3352	29.500	0.7438*	
15.0	0.0127	21.0	0.1208	26.323*	0.4197	30.137	0.8287*	
16.0	0.0204	22.0	0.1585	27.072*	0.4844	30.601	0.8910*	
17.0	0.0314	23.0	0.2039	27.540*	0.5277	30.971	0.9418	
18.0	0.0461	23.52	0.2312	28.289	0.6069	31.238	0.9816	
19.0	0.0654	24.68*	0.2992*	28.888	0.6709*	32.276	1.1452	

Table 10 Saturated vapor pressure of parahydrogen Рs, MPa [31].

Table 10T, K	Рs	
14	0.0079	
16	0.0215	
18	0.0481	
20	0.0933	
22	0.1632	
24	0.2642	
26	0.4029	
28	0.5861	
30	0.8214	
32	1.1185	

The data error for parahydrogen is ±0.25 %, and for orthohydrogen it has not been estimated, however, good convergence of most experimental data of different authors is noted.

At temperatures below the boiling point, the experimental data can be described by the following equation [32]:(10) lg Рs = A + B / T + C T,

where Рs — pressure, Pa; A, B, and C — constants, the values of which are given in Table 11.Table 11 Values of constants in the equation for lg Ps.

Table 11Constants	n-Н2	p-Н2	
А	6.79177	6.76882	
В	−44.95690	−44.34500	
С	0.020537	0.02039	

The above equation can also be used to calculate Ps at higher temperatures up to 28 K, but the calculation accuracy will be lower and the deviation of the calculated data from the experimental data will reach ±0.3 %. At temperatures above the boiling point, Рs should be calculated by the following equations [33,34]:(11) for n-Н2 lg Рs = 3.43703–31.875 / T + 2.39188 lg T,

(12) for р-Н2 lg Рs = 7.00632–50.009708 / (T + 1.0044) + 0.01748495 T,

where Рs — pressure, Pa.

The equations are valid in the temperature range of 20–29 K; and in the temperature range of 29–33 K, the obtained value should be adjusted as follows [34]:(13) Рs = 1.33445102 (T – 29)3–56.667 (T – 29)5 + 3.9648410−1 (T – 29)7.

4.1.6 Density

The density of solid hydrogen is 86.7 kg m−3 [35], liquid hydrogen — 71.07 kg m−3 [36] (at Т = 20.4 К, Р = 0.1 MPa), gaseous hydrogen — 0.0814 kg m−3 [17] (at Т = 298 К, Р = 0.1 MPa) [37]. Table 12, Table 13 show density of parahydrogen and normal hydrogen at saturation line.Table 12 Density of parahydrogen at saturation line at different temperatures, ρ, kg⋅m−3 [35].

Table 12T, K	ρ′*	ρ′′**	T, K	ρ′*	ρ′′**	T, K	ρ′*	ρ′′**	
14.0	76.77	0.139	20.0	71.11	1.243	26.0	62.80	4.97	
16.0	75.12	0.338	22.0	68.73	2.067	28.0	58.92	7.276	
18.0	73.22	0.688	24.0	66.00	3.246	30.0	53.85	10.861	
						32.0	45.70	17.648	

Table 13 Density of normal hydrogen at saturation line at different temperatures, ρ, kg⋅m−3 [37].

Table 13T, K	ρ′a	ρ′′b	T, K	ρ′a	ρ′′b	
13.947	77.07	0.128	22.0	69.15	1.997	
14.0	77.03	0.131	23.0	67.86	2.519	
15.0	76.23	0.211	24.0	66.47	3.143	
16.0	75.39	0.322	25.0	64.98	3.993	
17.0	74.50	0.559	26.0	63.37	4.763	
18.0	73.56	0.660	28.0	59.64	7.070	
19.0	72.56	0.901	30.0	54.86	10.504	
20.0	71.49	1.198	32.0	47.46	16.628	
21.0	70.36	1.560	33.099	37.68	26.106	
a — for liquid.

b — for vapor.

Dependences of density of liquid and gaseous normal hydrogen and parahydrogen on temperature and pressure are given in Table 12, Table 13.

The error of the experimental data in Table 12 is ± 0.1 %. The difference in density of parahydrogen based on the data of [35,37] for liquid does not exceed ±0.1 %, and for the gas phase, at some temperatures, it reaches ±1.0 %.

To determine the density of parahydrogen at saturation line, the equations of [35] for liquid (Р*) are recommended:(14) ρ*=ρp+14.763656ΔT0.38−0.88851066ΔT+1.33471250ΔT2/3−−0.58918594ΔT5/3+0.08080877ΔT2

for vapor at low pressures (Р**):(15) lg=P**−0.23872166.102+0.21129340.103T−1+0.13364318.102lgT−−0.19311670.104T−2+0.67461013.104T−3

for vapor at high pressures (Р**):(16) ρ**=ρP−14.5082613ΔT0.37+2,92222113ΔT+6.5322746ΔT0.7−8.9991918ΔT0.8

where ΔТ = Тcr – Т, К.

The density of normal liquid hydrogen at saturation line for the whole temperature range should be calculated by the following equation:(17) ρ=ρcr+∑n=14αn⋅(Tcr−T)n/3,

where ρcr and ρ — density at Tcr and Т at saturation line; n = 1, 2, 3, 4.

Values of αn for ρ, kg⋅m−3:αn	α1	α2	α3	α4	
n-Н2	13.3991990	2.0695229	0.17234364	0.1351370	
р-Н2	12.6349735	3.01856997	−0.26825918	−0.04176621	

The data calculated by Eqs. (14)–(17) differ from the experimental data by no more than ±0.1 %. The data error for the density of normal hydrogen is not reported in the literature.

Table 14, Table 15 show the density of normal hydrogen at different temperatures and pressures, ρ, kg. m−3.Table 14 Density of normal hydrogen at different temperatures and pressures, ρ, kg.m−3 [35].

Table 14Т, К	P, MPa	
0.1	0.2	0.6	1.0	1.6	2.0	3.0	4.0	
14	77.120	–	–	–	–	–	–	–	
16	75.475	75.559	75.929	76.303	76.826	77.150	77.925	78.686	
18	73.628	73.735	74.169	74.581	75.165	75.531	76.419	77.239	
20	71.512	71.639	72.152	72.620	73.306	73.735	74.719	75.645	
22	1.192	69.228	69.779	70.413	71.209	71.716	72.803	73.898	
24	1.075	2.318	67.153	67.876	68.850	69.443	70.809	71.997	
26	0.979	2.077	63.916	64.883	66.139	66.885	68.499	69.900	
28	0.902	1.887	59.749	61.200	62.939	63.957	65.945	67.603	
30	0.836	1.735	6.334	56.138	58.962	60.339	63.017	65.072	
40	0.616	1.251	4.021	7.267	13.594	19.478	36.949	46.525	
50	0.489	0.986	3.057	5.274	8.904	11.533	18.911	26.725	
60	0.406	0.816	2.491	4.226	6.937	8.815	14.297	18.805	
70	0.347	0.696	2.110	3.551	5.758	7.257	11.070	14.933	
80	0.304	0.608	1.834	3.072	4.949	6.212	9.385	12.560	
90	0.270	0.540	1.638	2.712	4.352	5.448	8.188	10.915	
100	0.243	0.485	1.457	2.430	3.890	4.862	7.286	9.683	

Table 15 Density of normal hydrogen at different temperatures and pressures, ρ, kg⋅m−3 [35].

Table 15T, K	P, MPa	
5.066	7.599	10.132	12.666	15.199	20.265	25.331	40.530	50.662	
20.34	75.888	77.980	79.692	81.262	82.700	85.020	87.08	–	–	
21.15	75.332	77.428	79.192	80.958	82.300	84.650	86.80	–	–	
22.15	74.750	76.800	78.650	80.420	81.760	84.250	86.43	–	–	
23.15	73.820	76.080	78.070	79.750	81.250	83.820	87.07	–	–	
24.15	73.160	75.350	77.430	79.350	80.730	83.340	85.63	91.50	–	
25.15	72.037	74.580	76.750	78.555	80.150	82.850	85.20	91.10	93.95	
26.15	71.370	73.900	76.140	77.960	79.570	82.330	84.75	90.70	93.60	
27.15	70.175	73.038	75.450	77.400	78.950	81.780	84.28	90.25	93.22	
28.15	69.250	72.070	74.670	76.670	78.300	81.200	83.62	89.85	92.90	
29.15	68.100	71.150	73.675	75.825	77.650	80.625	83.30	89.50	92.50	
30.15	66.870	70.150	73.000	75.070	76.950	80.000	82.80	89.05	92.15	
31.15	65.570	69.200	72.032	74.300	76.250	79.420	82.28	88.60	91.77	
32.15	64.150	68.100	71.100	73.450	75.500	78.770	81.75	88.15	91.40	
33.15	62.700	66.950	70.120	72.650	74.750	78.170	81.18	87.75	91.00	
34.15	61.075	65.840	69.100	71.750	73.950	77.550	80.59	87.25	90.62	
35.15	59.470	64.552	68.100	70.950	73.280	76.920	80.00	86.80	90.25	
36.15	57.850	63.370	67.130	69.950	72.400	76.250	79.450	85.400	89.900	
37.15	56.230	62.225	66.160	69.145	71.620	75.600	78.855	85.945	89.465	
38.15	54.600	61.050	65.295	68.250	70.735	74.950	78.275	85.500	89.075	
39.15	53.000	59.850	64.280	67.450	70.050	74.270	77.670	85.050	88.675	
40.15	51.400	36.680	63.270	66.525	69.265	73.625	73.055	84.610	88.300	
41.15	49.800	57.470	62.250	65.640	68.510	72.950	76.415	84.165	87.895	
42.15	48.175	56.250	61.250	64.790	67.715	72.235	75.770	83.725	87.490	
43.15	46.500	55.080	60.225	63.925	66.940	71.530	75.115	83.270	87.060	
45.15	43.100	52.575	98.200	62.150	65.350	70.080	73.810	82.370	86.250	
47.15	39.500	50.025	56.070	60.390	63.750	68.650	72.515	81.450	85.470	
49.15	35.650	47.650	54.000	58.615	62.200	67.230	71.250	80.525	84.680	
51.15	32.225	44.530	52.030	56.835	60.625	65.825	70.000	79.610	83.915	
53.15	29.365	41.835	50.050	55.005	59.065	64.450	68.750	73.650	83.105	
58.15	24.650	36.460	45.110	50.825	55.130	61.150	65.700	76.250	81.070	
63.150	21.902	32.630	40.667	46.645	51.300	57.900	62.790	73.830	79.000	
68.15	19.930	29.260	36.925	42.890	47.750	54.730	59.980	71.450	76.910	
73.15	19.250	26.475	33.325	39.312	44.600	52.150	57.420	69.135	74.785	
77.35	16.935	24.550	31.860	37.415	42.300	49.670	55.200	67.275	73.010	

4.1.7 Thermal conductivity

The thermal conductivity coefficient was measured under saturated vapor pressure [38]. The thermal conductivity of saturated liquid hydrogen does not depend on the ortho-para composition and in the temperature range from 16 to 24 K increases linearly with a temperature increase. This is confirmed by the results of measuring the thermal conductivity of single-phase hydrogen in a wide range of temperatures from 17 to 200 K and pressures up to 15 MPa [39]. Table 16 shows data on the thermal conductivity of saturated liquid parahydrogen.Table 16 Thermal conductivity of saturated liquid parahydrogen λ, mW⋅m−1⋅К−1 [40].

Table 16Т, К	17.0	19.5	22.0	25.0	30.0	
ρ, kg⋅m−3	74.16	71.59	68.73	64.79	53.93	
λ	91.1	96.2	99.9	99.7	86.7	

The thermal conductivity of normal liquid hydrogen depending on temperature can be described by the following equation [41]:(18) λ = 0.0712 + 0.002332 Т, W⋅ m−1⋅К−1

The root-mean-square deviation does not exceed ±1.6 %.

Table 17, Table 18 show data on the thermal conductivity of normal liquid hydrogen at saturation line.Table 17 Thermal conductivity of normal liquid hydrogena at saturation line, λ, mW⋅m−1⋅ К−1 [42].

Table 17T, K	λ′ n-Н2	T, K	λ′ n-Н2	T, K	λ′ n-Н2	
13.95	103.7	19.66	119.74	26	131.8	
14	103.8	20	117.8	27	134.0	
15	106.2	21	120.0	28	136.4	
16	108.6	21.16	120.16	29	139.0	
17	111.0	22	122.5	30	141.1	
17.85	115.56	23	125.0	31	143.5	
18	113.3	23.23	127.1	32	145.8	
18.97	117.65	24	127.7	33	148.1	
19	116.0	25	129.0	33.23	148.7	
a The thermal conductivity of parahydrogen differs from that of normal hydrogen by ±2 % [43].

Table 18 Thermal conductivity of normal liquid hydrogen λ, mW⋅m−1.К−1 [44].a

Table 18T, K	P, MPa	ρ, kg⋅m−3	λ	T, K	P, MPa	ρ, kg⋅m−3	λ	
16.976	4.271	77.995	104.0	27.337	4.763	69.166	117.8	
16.981	1.094	75.274	101.0	27.358	3.257	66.881	110.9	
16.985	2.270	76.357	99.1	27.380	0.709	60.932	98.0	
16.996	0.257	74.409	97.5	27.384	1.875	64.166	104.5	
19.591	5.715	77.164	112.6	29.724	0.118	0.999	24.0	
19.593	0.983	72.655	101.0	29.965	3.141	63.006	106.6	
19.595	2.939	74.742	104.5	29.971	4.139	65.034	110.9	
19.596	0.158	71.623	98.5	29.976	5.092	66.641	116.8	
19.605	7.042	78.160	113.5	29.981	1.278	56.933	92.0	
19.634	8.035	78.847	115.1	29.998	2.290	60.744	100.6	
19.672	9.069	79.518	117.0	40.315	4.631	49.138	92.4	
21.129	0.101	1.164	16.7	40.333	3.724	43.419	84.1	
21.373	0.083	1.005	16.7	40.340	2.660	30.135	57.1	
22.243	0.596	69.103	102.6	40.341	0.300	1.888	31.9	
22.251	6.080	75.371	119.8	40.350	1.505	12.144	42.7	
22.268	9.130	77.780	126.6	40.354	0.085	0.518	30.8	
22.272	4.327	73.716	121.8	40.356	2.847	33.239	71.6	
22.273	1.317	70.148	111.4	40.363	1.842	16.329	47.7	
22.286	3.182	72.478	116.4	40.371	0.916	6.443	36.0	
a The error of estimate does not exceed ±2 %.

Within the experimental error, the thermal conductivity of hydrogen does not depend on the ortho-para composition [44].

Table 19 shows data on the thermal conductivity of hydrogen at boiling and condensation lines.Table 19 Thermal conductivity of hydrogen at boiling and condensation lines λ, mW⋅m−1⋅К−1 [45].

Table 19T, K	13.8	14	16	18	20	22	
λ′	79.9	80.9	90.4	97.2	101.0	102.3	
λ′′	12.5	12.6	13.8	15.1	16.6	18.4	
Т, К	24	26	28	30	32		
λ′	101.5	99.9	94.9	89.4	84.3		
λ′′	20.6	23.5	27.6	33.9	48.8		

4.1.8 Fugacity

The fugacity of hydrogen can be calculated based on the averaged equation of state; the error of estimate is ±2 %. The calculation data are given in Table 20.Table 20 Fugacity of hydrogen ƒ, MPa.

Table 20T, K	P, MPa	
0.1	0.5	1.0	2.0	4.0	6.0	8.0	10.0	20.0	30.0	40.0	50.0	
14	0.01	0.01											
20	0.09	0.09	0.10	0.12	0.16	0.22	0.31	0.42	1.80				
30	0.10	0.42	0.62	0.71	0.92	1.18	1.49	1.86	5.37	14.33	36.41	89.25	
40	0.10	0.46	0.85	1.43	2.06	2.61	3.23	3.93	9.49	20.94	43.86	88.66	
50	0.10	0.48	0.92	1.70	2.92	3.92	4.89	5.94	13.25	26.34	49.45	89.44	
60	0.10	0.49	0.96	1.83	3.39	4.78	6.13	7.51	16.28	30.45	53.39	89.98	
70	0.10	0.49	0.97	1.90	3.65	5.31	6.95	8.60	18.56	33.43	56.02	89.99	
80	0.10	0.50	0.99	1.95	3.82	5.65	7.48	9.34	20.20	35.52	57.67	89.51	
90	0.10	0.50	0.99	1.98	3.92	5.86	7.82	9.83	21.34	36.94	58.61	88.67	
100	0.10	0.50	1.00	1.99	3.99	6.00	8.05	10.16	22.13	37.86	59.05	87.59	
120	0.10	0.50	1.00	2.01	4.06	6.16	8.31	10.53	23.01	38.75	59.00	85.08	
130	0.10	0.50	1.00	2.02	4.08	6.20	8.38	10.63	23.23	38.89	58.70	83.77	
150	0.10	0.50	1.01	2.03	4.11	6.25	8.45	10.73	23.42	38.86	57.83	81.19	
200	0.10	0.50	1.01	2.03	4.12	6.27	8.48	10.76	23.29	37.98	55.26	75.58	
300	0.10	0.50	1.01	2.02	4.10	6.22	8.40	10.62	22.58	36.03	51.13	68.07	
400	0.10	0.50	1.00	2.02	4.08	6.18	8.31	10.49	22.02	34.67	48.50	63.63	
500	0.10	0.50	1.00	2.02	4.06	6.14	8.26	10.40	21.63	33.74	46.78	60.79	

4.1.9 Viscosity

The dynamic viscosity of liquid and gaseous normal hydrogen and parahydrogen, including data for saturation line and critical region, can be calculated by the following equation [46]:(19) μΡ,Τ−μ0=0.0352⋅10−6ρ1–2.96/Τ–0.00888ρ,

where μР, Т and μ0 — viscosity of hydrogen at given Р and Т and at Т0 and Р0, 10−5 Pa⋅ s; ρ — density at given Р and Т, kg⋅ m−3;

Eq. (19) has physical sense at Т > Тtp. The calculated data are given in Table 21, Table 22.Table 21 Coefficient of dynamic viscosity of normal hydrogen and parahydrogen μ, 10−6 Pa s [46].

Table 21T, K	μ	T, K	μ	
n-Н2	p-Н2	n-Н2	p-Н2	
15	23.0	22.1	22	11.9	11.6	
16	20.4	19.7	23	11.0	10.8	
17	18.3	18.8	24	10.3	10.1	
18	16.6	16.0	25	9.6	9.3	
19	15.1	14.7	27	8.9	8.7	
20	13.9	13.5	28	–	7.5	
21	12.8	12.5	30	–	6.5	

Table 22 Coefficient of dynamic viscosity of parahydrogen and normal hydrogen in the liquid and gas phases at saturation line, μ, 10−6 Pa s [44].

Table 22T, K	p-Н2	n-Н2	T, K	p-Н2	n-Н2	
μ′	μ'′	μ′	μ'′	μ′	μ'′	μ′	μ'′	
14	23.10	0.76	24.50	0.76	26	8.26	1.52	8.46	1.49	
15	20.50	0.80	21.40	0.80	27	7.76	1.60	7.84	1.56	
16	18.40	0.86	19.10	0.86	28	7.16	1.69	7.29	1.65	
17	16.60	0.92	17.20	0.92	29	6.67	1.79	6.76	1.74	
18	15.10	0.98	15.60	0.98	30	6.17	1.90	6.27	1.86	
19	13.90	1.04	14.20	1.02	31	5.60	2.06	5.67	2.00	
20	12.70	1.11	13.10	1.09	31.5	5.31	2.16	5.35	2.09	
21	11.80	1.18	12.00	1.17	32.0	5.00	2.30	5.00	2.19	
22	10.90	1.26	11.20	1.24	32.5	4.60	2.52	4.54	2.35	
23	10.20	1.33	10.50	1.30	32.7	4.34	2.60	4.32	2.43	
24	9.45	1.39	9.70	1.37	32.9	3.46	3.46	–	–	
25	8.86	1.45	9.05	1.43	33.22	–	–	3.38	3.38	

The experimental values of hydrogen viscosity obtained by different researchers differ by ±15 %. Table 23, Table 24 shows smoothed values of the coefficient of dynamic viscosity obtained by the graphical averaging of the experimental data [47,48].Table 23 Coefficient of dynamic viscosity of gaseous hydrogen μ, 10−6 Pa s [48].

Table 23Т, К	μ	T, K	μ	T, K	μ	
19	0.510	80	3.579	293.16	8.80	
20	1.092	100	4.210	300	8.96	
22	1.21	120	4.792	373.16	10.33	
25	1.35	150	5.598	500	12.64	
30	1.61	180	6.349	750	16.60	
40	2.07	200	6.813	1,000	20.13	
50	2.49	230	7.489	1,073.16	21.03	
60	2.88	260	8.135	1,173.16	22.35	
70	3.237	273.16	8.430	1,273.16	23.55	

Table 24 Coefficient of dynamic viscosity of hydrogen at boiling and condensation lines μ, 10−7 Pa s [48].

Table 24T, K	13.8	14	16	18	20	22	24	26	28	30	32	
μ′	249.4	242.4	187.3	151.7	126.8	108.1	93.4	81.1	70.3	60.1	48.7	
μ″	6.7	6.8	7.5	8.1	8.8	9.6	10.7	12.2	14.2	17.3	23.0	

4.1.10 Diffusion

Table 25 shows the values of the coefficient of parahydrogen self-diffusion in orthohydrogen at P = 0.1 MPa.Table 25 Coefficient of parahydrogen self-diffusion in orthohydrogen D, 10−6 m2 s−1.

Table 25T, K	20.4	85.0	273.0	288.2	293.2	
D	0.8016 [49]	17.2 [49]	128.5 [49]	143.0 [50]	140 [51]	

To calculate the self-diffusion coefficient, it is recommended to use the following equation [49]:(20) lg D = a lg T + b.

The temperature dependence of the gas diffusion coefficient can be described by the following equation:(21) D = D0 (T/T0)m

The values of the D0 and m coefficients at P = 0.1 MPa are given in Ref. [49].

4.1.11 Compressibility factor

Table 26, Table 27 show data on the compressibility factor. The error of estimate of parahydrogen compressibility is ±0.1 % at temperatures below the critical one, and at higher temperatures, the error of the calculated data can reach several percent.Table 26 Compressibility factor of parahydrogen at saturation line, Ζ [50].

Table 26Т, К	Z′	Z″	Т, К	Z′	Z″	Т, К	Z′	Z″	
14	0.001739	0.98362	21	0.020631	0.89052	28	0.086392	0.69521	
15	0.002875	0.97597	22	0.026180	0.86960	29	0.103160	0.65475	
16	0.004362	0.96647	23	0.032778	0.84666	30	0.123360	0.60844	
17	0.006339	0.95508	24	0.040496	0.82158	31	0.148850	0.55280	
18	0.008852	0.94178	25	0.950800	0.79419	32	0.184890	0.47829	
19	0.012066	0.92659	26	0.059987	0.76424				
20	0.015959	0.90949	27	0.072173	0.73142				

Table 27 Compressibility factor of normal liquid hydrogen, Z [50].

Table 27Т, К	P, MPa	
1.013	2.096	3.039	4.053	6.079	8.106	10.132	12.158	
16	0.2022	0.3999	0.5941	0.7851	1.1590	–	–	–	
18	0.1835	0.3624	0.5370	0.7087	1.0440	1.3710	1.6950	2.002	
20	0.1693	0.3337	0.4936	0.6498	0.9542	1.2500	1.5390	1.821	
22	0.1587	0.3113	0.4595	0.6036	0.8838	1.1540	1.4160	1.676	
24	0.1510	0.2944	0.4332	0.5635	0.8290	1.0790	1.3210	1.559	
26	0.1457	0.2828	0.4137	0.5403	0.7841	1.0170	1.2430	1.464	
28	0.1431	0.2744	0.3988	0.5185	0.7471	0.9666	1.1790	1.382	
30	0.1456	0.2708	0.3890	0.5026	0.7185	0.9255	1.1240	1.316	
32	–	0.2732	0.3848	0.4919	0.6965	0.8912	1.0790	1.261	
33	–	0.2781	0.3845	0.4876	0.6869	0.8757	1.0580	1.235	

The averaged equation of state should be used to calculate the compressibility factor:(22) Z=PVRT,

where R — gas constant, J mol−1.

4.1.12 Isobaric expansion coefficient

Table 28 shows the values of the isobaric expansion coefficient of normal liquid hydrogen and parahydrogen.Table 28 Isobaric expansion coefficient of parahydrogen and normal hydrogen αt, К−1 [51].

Table 28T, К	αt (n-H2)	αt (p-H2)	T, К	αt (n-H2)	αt(p-H2)	
14	0.00972	0.00975	20.38	0.01543	0.01561	
15	0.01062	0.01066	36	0.02980	0.02930	
16	0.01151	0.01158	38	0.02790	0.02760	
17	0.01241	0.01250	260	0.00380	0.00380	
18	0.01330	0.01342	280	0.00360	0.00360	
19	0.01420	0.01434	500	0.00200	–	
20	0.01509	0.01526	550	0.00180	–	

The isobaric expansion coefficient of gaseous hydrogen in the temperature range of 273–373 K and at a pressure of 0.1013 MPa is 0.003660 K-1, and at a pressure of 0.1456 MPa is 0.003659 K-1 [45]. The data error is not specified.

The average value of the isobaric expansion coefficient of hydrogen can be approximately determined by the following equation [51]:(23) αt=ρ12−ρ222(T2−T1)⋅ρ1⋅ρ2

where ρ1 and ρ2 — hydrogen density at Т1 and Т2, respectively.

The error of estimate is ±1 %.

4.1.13 Isothermal compressibility coefficient

Table 29 shows the calculated values of the isothermal compressibility coefficient of parahydrogen and normal hydrogen.Table 29 Isothermal compressibility coefficient βP, MPa−1.

Table 29P, MPa	βP(n-Н2)	βP(p-Н2)	P, MPa	βP(n-Н2)	βP(p-Н2)	P, MPa	βP(n-Н2)	P, MPa	βP(p-Н2)	
T = 36 K	T = 50 K	T = 75 K	T = 300 K	
1.0	0.1359	0.1385	2.0	0.0593	0.0590	9	0.0094	9	0.0105	
1.2	0.1263	0.1311	2.2	0.0548	0.0544	10	0.0080	10	0.0094	
9.0	0.0021	0.0021	9.0	0.0052	0.0053	15	0.0041	15	0.0061	
10.0	0.0019	0.0019	10.0	0.0043	0.0043	20	0.0025	20	0.0044	

At saturation line at Р = 0.1 MPa for parahydrogen at Т = 16 К, βP = 0.0122 MPa−1, at 18 К, βP = 0.0139 MPa−1 [36]. The researchers do not provide the data error. To calculate βP, it is recommended to use the following equation [36]:(24) βP=V0−VV0(P−P0)

where V, V0 — specific volume of hydrogen at pressure P and P0, respectively.

4.1.14 Isochoric pressure coefficient

Table 30 shows the calculated values of the isochoric pressure coefficient of parahydrogen in the liquid and gaseous states [52].Table 30 Isochoric pressure coefficient of parahydrogen γ, К−1 [52].

Table 30T, K	P, MPa	
0.01	0.1	0.5	1.0	2.0	4.0	
14	91.236	9.1380	1.8400	–	–	–	
15	0.0683	9.0173	1.8148	0.9141	0.4531	–	
16	0.0638	8.9670	1.8059	0.9103	0.4619	0.2366	
18	0.0564	8.8069	1.7780	0.8988	0.4582	0.2366	
20	0.0506	8.4849	1.7186	0.8784	0.4472	0.2330	
22	0.0459	0.0508	1.6273	0.8298	0.4290	0.2259	
26	0.0387	0.0415	1.3516	0.7048	0.3758	0.2050	
30	0.0335	0.0352	0.0460	0.506	0.3015	0.1774	
40	0.0251	0.0257	0.0288	0.0340	0.0536	0.0911	
60	0.0167	0.0168	0.0176	0.0185	0.0206	0.0251	
80	0.0125	0.0126	0.0129	0.0132	0.0139	0.0153	
100	0.0100	0.0100	0.0102	0.0103	0.0107	0.0113	
200	0.00500	0.00504	0.00502	0.00503	0.00506	0.00512	
T, K	P, MPa	
6.0	10.0	15.0	20.0	25.0	30.0	
300	0.3379	0.34030	0.34260	0.34430	0.34550	0.34620	
400	0.25150	0.25230	0.25310	0.25360	0.25400	0.25420	
500	0.20057	0.20088	0.20115	0.20133	0.20141	0.20140	
600	0.10688	0.16699	0.16707	0.16711	0.16709	0.16703	
700	0.14292	0.14294	0.14294	0.14292	0.14287	0.14279	
800	0.12499	0.12498	0.12494	0.12490	0.12483	0.12475	
900	0.11107	0.11104	0.11090	0.11093	0.11066	0.11079	
1,000	0.09996	0.09991	0.09985	0.09979	0.09973	0.09966	
1,100	0.09085	0.09081	0.09075	0.09070	0.09063	0.09057	
1,200	0.08327	0.08323	0.08318	0.08313	0.08306	0.08301	
1,300	0.07687	0.07683	0.07677	0.07673	0.07667	0.07662	
1,400	0.07137	0.07134	0.07129	0.07124	0.07119	0.07114	
1,500	0.06661	0.06658	0.06653	0.06649	0.06644	0.06640	

At a temperature T ≥ 300 K, the values of γ 102 are given. The data error is not specified. The expansion, compressibility and pressure coefficients are related to each other by the following equation [53]:(25) γ=αt/(βP⋅Ρ).

4.1.15 Sound velocity in hydrogen

Sound velocity in parahydrogen at solidification line is given in Table 30, at saturation line — in Table 31, Table 32.Table 31 Sound velocity in parahydrogen at solidification line а, m ⋅ s−1 [54].

Table 31T, K	14	15	16	17	18	19	20	21	22	23	
a	1,267.5	1,353.6	1,442.6	1,528.0	1,603.9	1,669.5	1,726.7	1,777.3	1,822.0	1,860.9	

Table 32 Sound velocity in parahydrogen at saturation line а, m ⋅ s−1 [54].

Table 32T, K	14	16	18	20	22	
a′	1,366.8	1,271.6	1,185.5	1,110.7	1,038.2	
a′′	307.0	325.1	340.2	352.6	362.2	
T, K	24	26	28	30	32	
a ′	961.0	874.4	773.8	653.2	498.1	
a′′	369.3	373.3	376.0	375.7	372.8	

Table 33 shows data on sound velocity in normal hydrogen at saturation line (liquid phase).Table 33 Sound velocity in normal hydrogen at saturation line (liquid phase) α, m⋅s−1.

Table 33T, K	14	16	18	20	22	24	26	28	30	
a′	1,265a	1,226a	1,182a	1,132a	1,103b	1,003.5b	925.0b	829.0b	708.0b	
a Data from [35].

b Data from Ref. [37].

The error of estimate of sound velocity according to Ref. [1] is ±2 % for liquid and ±1 % for gas; in other works, it is not specified.

Sound velocity in liquid hydrogen can be calculated using the following equation:(26) a=g⋅βP−1⋅ρ−1

where a — sound velocity, m⋅ s−1; βP — isothermal compressibility coefficient, Pa−1; ρ — density, kg⋅m−3; g — gravity acceleration, m⋅ s−2.

Sound velocity in liquid n-Н2 and р-Н2 can be described by the following empirical equation with an error of 0.2–0.6 m s−1 [54]:(27) a=a0+bP+cP2+dp3+eP4+⋯,

where a0, b, c, d, e − coefficients, the values of which are presented in Table 34.Table 34 Values of the coefficients in Eq. (27).

Table 34T, K	a0, m⋅s−1	b, 10−5 m s−1 Pa−1	c, 10−12 m s−1 Pa−2	
n-Н2	p-Н2	n-Н2	p-Н2	n-Н2	p-Н2	
16.74	1,206.8	1,202.0	4.1231	4.2331	−1.5359	−2.9176	
18.25	1,173.0	1,167.8	4.5791	4.4220	−2.2844	−1.7381	
19.17	1,148.5	1,144.8	4.7848	4.7951	−2.1721	−2.0800	
20.50	1,112.3	1,108.0	5.0739	5.0577	−2.1268	−2.0296	
T, K	d, 10−19 m s−1 Pa-3	e, 10−26 m s−1 Pa−4	
n-Н2	p-Н2	n-Н2	p-Н2	
16.74	0.4428	4.0279	0.0590	−2.4346	
18.25	1.2892	0.7299	−0.3488	−0.1633	
19.17	0.9130	0.8116	−0.1714	−0.1419	
20.50	0.7196	0.6452	−0.1037	−0.0871	

In the temperature range of 15–30 K with an error of ±0.5 %, sound velocity in liquid hydrogen can be calculated by the following equations:(28) in normal hydrogen a = − 616.5 + 0.0492 ρliq

(29) in parahydrogen a = − 627.6 + 0.0494 ρliq,

where ρliq — density of liquid hydrogen, mol⋅m−3.

Table 35 shows the values of sound velocity in normal hydrogen and parahydrogen.Table 35 Sound velocity in normal hydrogen а, m⋅s−1 [54].

Table 35Т, К	P, MPa	
0.1	0.5	1.0	2.0	4.0	6.0	8.0	10.0	20.0	30.0	50.0	
15	1,245.3	1,260.3	1,278.4	1,312.6	–	–	–	–	–	–	–	
20	1,135.8	1,156.4	1,180.7	1,225.3	1,302.7	1,369.2	1,428.1	1,481.1	1,687.0	–	–	
30	447.8	417.7	765.2	898.9	1,057.1	1,165.3	1,250.9	1,323.2	1,588.5	1,774.2	–	
40	521.3	509.3	495.2	483.0	728.0	925.9	1,057.6	1,158.4	1,486.7	1,705.8	2,026.7	
50	334.5	579.8	575.5	574.0	628.6	758.3	891.3	1,004.6	1,377.6	1,615.5	1,962.4	
60	640.2	639.1	638.9	643.3	675.7	743.6	832.8	925.1	1,292.1	1,540.9	1,895.0	
80	733.4	735.4	738.6	747.2	773.8	811.8	859.6	914.7	1,204.7	1,444.6	1,804.8	
100	808.8	811.9	816.4	826.0	850.6	881.1	916.5	955.8	1,181.2	1,393.3	1,737.4	
120	873.4	877.0	881.6	891.6	914.8	941.5	971.2	1,003.1	1,184.3	1,368.3	1,681.6	
140	932.1	935.8	940.5	950.6	972.6	997.1	1,023.4	1,051.3	1,204.6	1,365.3	1,651.3	
160	987.3	991.0	995.8	1,005.7	1,026.9	1,049.7	1,073.9	1,099.1	1,234.4	1,376.6	1,640.3	
180	1,039.8	1,043.5	1,048.3	1,058.0	1,078.0	1,100.0	1,122.0	1,143.8	1,266.8	1,396.8	1,641.7	
200	1,090.2	1,094.0	1,098.7	1,108.2	1,127.9	1,148.5	1,169.8	1,191.6	1,305.5	1,422.7	1,651.3	
250	1,209.4	1,212.5	1,217.0	1,226.0	1,244.3	1,263.0	1,282.0	1,301.3	1,400.0	1,499.3	1,695.2	
300	1,319.3	1,322.7	1,327.0	1,335.5	1,352.6	1,370.0	1,382.4	1,404.9	1,493.6	1,581.9	1,754.4	
350	1,422.5	1,425.8	1,429.8	1,437.8	1,454.0	1,470.1	1,468.4	1,502.6	1,334.0	1,664.6	1,821.1	
400	1,519.6	1,522.7	1,528.5	1,534.1	1,549.4	1,564.6	1,579.8	1,595.1	1,670.8	1,745.4	1,889.6	
600	1,859.1	1,961.6	1,864.7	1,871.0	1,883.6	1,896.2	1,908.6	1,921.0	1,982.1	2,041.4	2,155.4	
800	2,142.1	2,144.3	2,147.0	2,152.4	2,163.2	2,173.9	2,184.5	2,195.1	2,247.8	2,297.9	2,394.7	
1,000	2,386.0	2,387.9	2,390.2	2,395.0	2,404.4	2,413.8	2,423.2	2,432.5	2,478.4	2,523.1	2,608.4	
1,500	2,886.6	2,888.1	2,890.0	2,893.6	2,901.0	2,908.3	2,915.5	2,922.8	2,958.7	2,903.9	3,061.6	

The differences in the values of sound velocity in normal hydrogen and parahydrogen in the liquid phase are approx. ±1.0 %, and even less in the gas phase.

5 Thermodynamic properties

Thermodynamic characteristics are the property of a system to accumulate, release, or transform the energy (mainly thermal, internal) of the system depending on the processes occurring in this system.

Hydrogen is the lightest element, and this explains some of its unusual thermodynamic characteristics. The moment of inertia of the H2 molecule is 10 or more times lower than the moment of inertia of other two-atom molecules.

The properties (including thermodynamic characteristics) of hydrogen are further complicated by the fact that it has three isotopes: stable ortho- and para hydrogen and tritium. Each of them has a nuclear spin. Two nuclei with spins in the same molecule form a quantized system. In the H2 molecule, spins equal to 1/2 are combined into parallel or antiparallel systems. In the absence of the possibility for catalytic transformation, the nature of spin orientation in the molecule changes very rarely. Consequently, hydrogen consists of two kinds of particles with a constant ratio. An ordinary symmetric two-atom molecule has rotational energy levels corresponding only to either even or odd values of the rotational quantum number (symmetric or asymmetric states). In most cases, the macroscopic properties of substances are essentially independent of the symmetry or asymmetry of the molecular state. However, for hydrogen, due to relatively large intervals in the values of rotational energy, there is a significant difference in the thermodynamic characteristics of symmetric and asymmetric states. The observed thermodynamic characteristics of hydrogen depend on the relative amounts and determine differences in thermal conductivity, heat capacity, etc.

The state with even values of the rotational quantum number, having antiparallel orientation of nuclear spins, is called para hydrogen, and the other state with parallel spins and odd values of the rotational quantum number is called ortho hydrogen. Since the lowest rotational level has zero rotational quantum number, the para state is stable at low temperatures. It has been found, however, that the state with parallel spins is relatively three times more likely than the state with antiparallel spins, therefore, under equilibrium conditions at high temperature, there is three times more ortho hydrogen than para hydrogen. Ordinary hydrogen is a mixture of 1/4 para hydrogen and 3/4 ortho hydrogen. The estimated values of thermodynamic characteristics for each hydrogen type were calculated using the corresponding molecular characteristics in the corresponding relations. The calculation results are in good agreement with the experimental data.

The uninhibited (catalytic) transformation of ortho-, para modifications was analyzed, and the thermodynamic characteristics of the equilibrium mixture were calculated using formulas for chemical equilibrium.

The heat capacity of solid hydrogen was measured by several researchers, the individual measurements are in good agreement and presented as tabular data. The presented data show that, at temperatures above 11–12 K, the heat capacity of solid hydrogen does not depend much on the ortho-para composition, but at lower temperatures sharp differences occur. This can be explained by the fact that solid hydrogen at 12–14 K consists of freely rotating molecules, and at lower temperatures interaction between them becomes significant (compared to kT). At 12 K, almost all the molecules of para hydrogen are in the state with zero rotational quantum number, therefore, the heat capacity of solid para hydrogen is determined only by the linear vibrations of the molecules in the lattice. At 12 K, ortho molecules are chaotically distributed by nine states resulting from three possible components of the nuclear spin and three components of the molecule's momentum relative to a given axis.

In view of the above, it should be borne in mind that extrapolation to 0 K of the experimental heat capacity makes it possible to determine the value of practical entropy, which does not take into account the orientation of nuclear spins (as well as the effect of isotope mixing). In the case of a proton with spin 1/2, the entropy determined by the spin orientation is R 1n 2 per proton or 2R 1n 2 for two protons in the H2 molecule. Consequently, on a practical level, the entropy of hydrogen used in combination with the entropies of other substances is by 2R 1n 2 = 2.75 cal/deg • mol less than the entropy calculated based on spectroscopic data taking into account ortho- and para components.

5.1 Enthalpy

Table 36, Table 37, Table 38, Table 39, Table 40 show the calculated values of specific enthalpy of normal hydrogen and parahydrogen. Table 39 shows the values for enthalpy of gaseous hydrogen. The temperature of 293.16 K (or conventionally 293 K) is taken as the zero of enthalpy (physical heat content) [1].Table 36 Enthalpy of liquid and gaseous normal hydrogen at saturation line Н, kJ⋅kg−1 [1].

Table 36T, K	Р, 105 Pa	Н′	Н″	T, K	Р, 105 Pa	Н′	Н″	
13.95	0.0723	217.503	669.459	24	2.5737	307.525	732.224	
14	0.0745	217.647	669.949	25	3.2062	320.111	733.708	
15	0.1274	221.901	679.002	26	3.9414	334.193	732.947	
16	0.2054	228.507	687.647	27	4.7887	350.046	730.911	
17	0.3150	236.704	695.805	28	5.7549	376.859	726.876	
18	0.4629	245.854	703.392	29	6.8483	387.781	720.351	
19	0.6561	255.484	710.328	30	8.0777	410.088	710.499	
20	0.9022	265.319	716.530	31	9.4548	435.657	695.659	
21	1.2086	275.277	721.917	32	10.9968	467.529	671.637	
22	1.5836	285.455	726.398	33	12.7314	521.912	617.902	
23	2.0358	296.095	729.872	33.1	12.9169	532.763	605.478	

Table 37 Enthalpy of liquid and gaseous normal hydrogen at pressure P = 0.1 MPa; Н, kJ⋅kg−1 [1].

Table 37Т, К	Н	Т, К	Н	Т, К	Н	Т, К	Н	Т, К	Н	
14	211	26	781	40	933	120	1,804	260	3,658	
16	226	28	803	50	1,038	140	2,048	280	3,941	
18	241	30	825	60	1,142	160	2,298	300	4,227	
20	274	32	847	70	1,248	180	2,559	350	4,946	
22	736	34	869	80	1,354	200	2,826	400	5,657	
24	759	36	890	90	1,463	220	3,099	450	6,378	
		38	911	100	1,573	240	3,376	500	7,104	

Table 38 Enthalpy of liquid and gaseous parahydrogen at saturation line H [1].

Table 38T, K	Н′	Н″	Н′	Н″	
kJ⋅kmol−1	kJ⋅kg−1	
14	−621.06	286.97	−308.07	142.35	
15	−607.40	305.10	−301.30	151.34	
16	−592.96	322.39	−294.14	159.92	
17	−577.78	338.76	−286.61	167.99	
18	−561.65	353.76	−278.60	175.48	
19	−544.28	367.52	−269.99	182.31	
20	−525.46	379.75	−260.65	188.37	
21	−506.08	390.29	−250.54	193.60	
22	−483.06	398.95	−239.62	197.90	
23	−459.35	405.52	−227.86	201.16	
24	−433.86	409.74	−215.21	203.25	
25	−406.46	411.32	−201.62	204.03	
26	−376.95	409.85	−186.98	203.30	
27	−344.99	404.86	−171.13	200.83	
28	−310.07	395.62	−153.81	196.25	
29	−271.35	381.83	−134.21	190.50	
30	−227.36	359.14	−112.78	178.15	
31	−175.06	325.91	−86.84	161.67	
32	−106.01	270.05	−52.59	133.96	

Table 39 Enthalpy of parahydrogen in the single-phase region Н, kJ⋅kmol−1 [1].

Table 39T, K	P, MPa	
0.1	0.5	1.0	2.0	4.0	6.0	8.0	10.0	20.0	30.0	
14	−619	−610	–	–	–	–	–	–	–	–	
16	−591	−584	−572	−550	−506	−462	–	–	–	–	
18	−561	−552	−542	−521	−478	−435	−392	−349	–	–	
20	−525	−518	−508	−488	−447	−405	−363	−321	−110	–	
22	424	−477	−469	−450	−411	−371	−330	−289	−81	125	
24	469	−431	−424	−408	−372	−334	−294	−253	−49	155	
26	514	−376	−372	−360	−329	−293	−255	−216	−15	187	
28	559	436	−312	−306	−282	−249	−214	−176	20	220	
30	602	499	−234	−245	−231	−203	−170	−135	57	254	
32	646	556	374	−171	−175	−153	−124	−91	95	290	
34	689	609	473	−70	−114	−101	−76	−46	134	326	
36	731	660	548	109	−45	−44	−25	2.5	175	364	
38	775	710	614	314	35	17	30	53	218	403	
40	818	759	675	497	124	84	88	107	262	445	
42	860	806	731	544	221	154	148	162	308	487	
44	903	853	785	626	322	229	212	220	355	530	
46	946	900	838	698	419	307	278	280	404	575	
48	988	945	888	763	511	386	346	341	453	620	
50	1,031	990	938	824	596	465	416	404	504	667	
60	1,245	1,215	1,177	1,100	952	836	766	732	771	912	
70	1,465	1,441	1,412	1,355	1,249	1,160	1,095	1,055	1,055	1,174	
80	1,695	1,677	1,634	1,609	1,528	1,460	1,406	1,369	1,350	1,451	
90	1,941	1,926	1,907	1,872	1,808	1,755	1,712	1,680	1,654	1,743	
100	2,203	2,190	2,175	2,147	2,096	2,054	2,020	1,994	1,971	2,051	
110	2,482	2,472	2,460	2,437	2,396	2,363	2,336	2,315	2,298	2,373	
120	2,777	2,769	2,759	2,740	2,707	2,681	2,660	2,645	2,637	2,711	
130	3,089	3,082	3,074	3,059	3,033	3,013	2,997	2,986	2,989	3,063	
140	3,405	3,400	3,394	3,382	3,363	3,346	3,335	3,338	3,342	3,417	
150	3,727	3,723	3,718	3,709	3,694	3,683	3,676	3,672	3,696	3,77З	
160	4,053	4,051	4,046	4,039	4,028	4,021	4,017	4,017	4,050	4,131	
170	4,382	4,379	4,376	4,371	4,364	4,360	4,359	4,361	4,403	4,488	
180	4,710	4,709	4,707	4,704	4,700	4,699	4,700	4,704	4,755	4,843	
190	5,041	5,040	5,038	5,037	5,036	5,038	5,041	5,048	5,106	5,198	
200	5,370	5,370	5,369	5,369	5,371	5,374	5,380	5,388	5,453	5,549	
T, K	P, MPa	
0.1	0.5	1.0	2.0	4.0	6.0	7.0	8.0	10.0	20.0	30.0	
220	6,015	6,015	6,016	6,019	6,024	6,032	6,042	6,053	6,130	6,233		
240	6,643	6,695	6,646	6,651	6,660	6,671	6,677	6,683	6,697	6,785	6,894	
260	7,261	7,263	7,266	7,272	7,284	7,298	7,305	7,313	7,329	7,425	7,540	
280	7,870	7,873	7,876	7,873	7,898	7,914	7,923	7,931	7,950	8,053	8,173	
300	8,471	8,474	8,478	8,487	8,504	8,522	8,531	8,541	8,561	8,671	8,796	
350	9,956	9,960	9,966	9,976	9,998	10,020	10,031	10,043	10,066	10,190	10,324	
400	11,428	11,432	11,439	11,451	11,475	11,500	11,513	11,526	11,551	11,685	11,827	
450	12,894	12,900	12,906	12,920	12,947	12,974	12,988	13,001	13,029	13,171	13,318	
500	14,359	14,365	14,372	14,386	14,415	14,444	14,458	14,473	14,502	14,650	14,602	
550	15,824	15,830	15,838	15,865	15,683	15,913	15,928	15,943	15,974	16,127	16,263	
600	17,290	17,297	17,304	17,320	17,351	17,383	17,398	17,414	17,445	17,603	17,762	
650	18,760	18,766	18,774	18,790	18,822	18,855	18,871	18,887	18,919	19,080	19,242	
700	20,231	20,237	20,245	20,262	20,295	20,328	20,344	20,361	20,393	20,558	20,722	
750	21,706	21,713	21,722	21,738	21,772	21,805	21,822	21,839	21,872	22,039	22,205	
800	23,188	23,195	23,203	23,220	23,254	23,288	23,305	23,322	23,373	23,524	23,692	
850	26,474	24,681	24,689	24,707	24,741	24,775	24,793	24,810	24,844	25,014	25,184	
900	26,166	26,173	26,182	26,199	26,234	26,268	26,286	26,303	26,337	26,509	26,680	
1,000	29,168	29,175	29,184	29,281	29,236	29,272	29,289	29,307	29,342	29,516	29,688	
1,100	32,211	32,218	32,227	32,245	32,281	32,314	32,333	32,352	32,387	32,563	32,737	
1,200	35,292	35,300	35,309	35,327	35,362	35,396	35,416	35,434	35,460	35,646	35,821	
1,300	38,410	38,417	38,426	38,444	38,480	38,516	38,534	38,552	38,587	38,765	38,941	
1,400	41,571	41,578	41,587	41,605	41,641	41,677	41,695	41,713	41,749	41,927	42,103	
1,500	44,789	44,796	44,605	44,823	44,859	44,895	44,913	44,931	44,967	45,145	45,321	

Table 40 Enthalpy of gaseous hydrogen at P = 0.1 MPa, calculated from 0 K, Н, kJ⋅kg−1 [1].

Table 40Т, К	298.16	300	400	500	600	
Н	4.203	4.230	5.673	7.123	8.576	
Т, К	700	900	1,100	1,300	1,500	
Н	10.036	12.976	15.975	19.051	22.210	

5.2 Entropy

Table 41, Table 42 show the values of entropy of liquid and gaseous parahydrogen at saturation line and in the single-phase region at different temperatures and pressures.Table 41 Entropy of liquid and gaseous parahydrogen at saturation line S, kJ.kg−1⋅К−1 [1].

Table 41T, K	S′	S″	T, K	S′	S″	
14	5.703	38.229	24	10.780	28.205	
15	6.971	36.699	25	11.294	27.509	
16	7.027	35.353	26	11.772	26.821	
17	7.474	34.165	27	12.367	26.131	
18	7.919	33.100	28	12.938	25.428	
19	8.370	32.136	29	13.544	24.692	
20	8.830	31.251	30	14.207	23.896	
21	9.302	30.429	31	14.970	22.980	
22	9.784	29.655	32	15.954	21.780	
23	10.277	28.917				

Table 42 Entropy of normal hydrogen at saturation line S, kJ⋅kg−1⋅К−1 [1].

Table 42T, K	S′	S″	T, K	S′	S″	
13.95	14.230	46.635	24	19.748	36.440	
14	14.240	46.548	25	19.223	35.780	
15	14.528	45.001	26	19.730	35.267	
16	14.947	43.643	27	20.277	34.383	
17	15.435	42.441	28	20.868	33.682	
18	15.946	41.362	29	21.500	32.968	
19	16.452	40.392	30	22.1812	32.195	
20	16.939	39.500	31	22.934	31.322	
21	17.404	38.673	32	23.847	30.226	
22	17.853	37.895	33	25.396	28.304	
23	18.296	37.156	33.1	25.709	27.906	

Table 43, Table 44 show the values of entropy of normal hydrogen at saturation line and in the single-phase region at different temperatures and pressures.Table 43 Entropy of liquid and gaseous normal hydrogen S, kJ⋅kg−1⋅К−1 [1].

Table 43T, K	S	T, K	S	T, K	S	
14	8.17	36	39.79	180	57.84	
16	9.09	38	40.37	200	59.24	
18	10.04	40	40.91	220	60.55	
20	10.99	50	43.25	240	61.75	
22	34.38	60	45.17	260	62.88	
24	35.36	70	46.79	280	63.68	
26	36.25	80	48.21	300	64.90	
28	37.07	90	49.48	350	67.13	
30	37.83	100	50.65	400	69.11	
32	38.53	140	54.62	450	70.76	
34	39.19	160	56.29	500	72.30	

Table 44 Entropy of parahydrogen at boiling and condensation lines S, kJ⋅kg−1⋅К−1 [1].

Table 44T, K	S′	S″	T, K	S′	S″	
13.8	4.959	37.482	24	9.792	27.169	
14	5.068	37.150	26	10.824	25.815	
16	6.031	34.286	28	11.937	24.448	
18	6.936	32.037	30	13.208	22.927	
20	7.859	30.189	32	14.940	20.778	
22	8.809	28.600				

5.3 Heat capacity

The heat capacity of liquid hydrogen at saturation line can be calculated by the following equation [55,56]:(30) Сs = [АТ (То – Т)−n + В + СТ + DТ2 + ЕТ3 + FT4 + GT5] ⋅ 2.07709,

where То = 32.984 K; n = 0.10; А = 1.6815742; В = −32.802789; С = 6.8169871;D = −0.73194341; Е = 0.033574357; F = −7.6829740 ⋅ 10−4; G = 6.9029224 ⋅ 10−6

The difference in the heat capacity of ortho- and parahydrogen (excluding conversion heat) does not exceed the error of estimate. Table 45, Table 46, Table 47, Table 48 show the values of specific heat capacity for different states of hydrogen.Table 45 Isochoric (CV) and isobaric (Cp) heat capacity of gaseous parahydrogen at saturation line, kJ⋅kg−1⋅К−1 [55].

Table 45T, K	P, kPa	Сv′′	Cр″	T, K	P, kPa	Сv′′	Cр″	
13.800*	7.0	6.21	10.52	20.268*	101.3	6.50	12.15	
14	7.9	6.21	10.54	22	163.4	6.61	13.03	
15	13.4	6.24	10.67	24	264.5	6.74	14.49	
16	21.6	6.27	10.85	26	403.5	6.89	16.85	
17	32.9	6.32	11.07	28	587.1	7.11	21.24	
18	48.2	6.37	11.34	30	822.5	7.50	31.99	
19	68.2	6.43	11.66	32	1,119.8	8.11	87.02	
20	93.5	6.49	12.04	32.976*	1,292.8	–	–	

Table 46 Isobaric and isochoric heat capacity of parahydrogen and adiabatic indexa at solidification and saturation lines, kJ⋅kg−1⋅К−1 [56].

Table 46T, K	Solidification line	Saturation line	
Cp	Cv	k	Cp″	Сp′	Cv″	Сv′	к′′	к″	
14	6.464	4.792	208.12	6.520	10.735	4.782	6.082	15,114.7	1.677	
15	6.439	4.899	38.72	6.908	10.548	4.940	6.154	8,481.7	1.672	
16	6.269	4.803	23.58	7.231	10.723	4.963	6.205	5,094.9	1.668	
17	6.149	4.722	17.91	7.603	10.903	4.989	6.232	3,210.6	1.668	
18	6.186	4.783	14.82	8.109	11.108	5.110	6.243	2,088.1	1.670	
19	6.361	4.974	12.80	8.738	11.351	5.313	6.246	1,391.0	1.675	
20	6.607	5.234	11.34	9.447	11.653	5.547	6.248	946.3	1.681	
21	6.862	5.498	10.23	10.201	12.029	5.650	6.257	656.0	1.689	
22	7.086	5.725	9.34	10.089	12.509	5.960	6.278	462.3	1.699	
23	7.261	5.889	8.60	11.820	13.120	6.104	6.313	330.1	1.710	
24				12.730	13.902	6.204	6.365	238.2	1.724	
25				13.750	14.913	6.268	6.365	172.9	1.740	
26				14.975	16.244	6.305	6.517	125.9	1.760	
27				16.518	18.048	6.327	6.617	91.4	1.785	
28				18.594	20.602	6.342	6.734	65.9	1.819	
29				21.626	24.464	6.398	6.864	46.8	1.868	
30				26.605	30.965	6.399	7.010	32.3	1.940	
31				36.580	44.250	6.469	7.166	21.2	2.062	
32				67.503	86.684	6.616	7.324	12.6	2.317	
a In the table, the adiabatic index к = (–СР/СV) (∂P/∂V) ⋅Tv/p.

Table 47 Isobaric and isochoric heat capacity of normal hydrogen at boiling and condensation lines, kJ⋅kg−1.К−1 [57].

Table 47T, K	Boiling line	Condensation line	
CP′	СV′	CP″	СV″	
13.8	7.719	5.440	10.672	6.317	
14	7.524	5.247	10.696	6.325	
16	7.296	4.786	11.011	6.402	
18	8.255	5.189	11.469	6.489	
20	9.485	5.617	12.129	6.588	
22	10.881	5.942	13.098	6.704	
24	12.574	6.178	14.577	6.846	
26	14.891	6.368	16.999	7.028	
28	18.650	6.559	21.519	7.273	
30	26.839	6.827	32.563	7.628	
32	69.276	7.398	96.302	8.222	

Table 48 Isobaric heat capacity of normal hydrogen at saturation line Ср, kJ⋅kg−1⋅К−1 [58].

Table 48T, K	Ср′	Ср″	T, K	Ср′	Ср″	
14	6.65	10.37	24	12.71	13.71	
15	6.99	10.53	25	13.73	14.65	
16	7.34	10.69	26	14.92	15.88	
17	7.69	10.87	27	16.40	17.53	
18	8.17	11.06	28	18.36	19.85	
19	8.77	11.29	29	21.15	23.27	
20	9.45	11.58	30	25.56	28.87	
21	10.20	11.94	31	33.84	39.65	
22	10.98	12.40	32	55.80	69.09	
23	11.81	12.97	33	277.93	405.61	

5.4 Enthalpy of formation

The enthalpy of formation of hydrogen at 293.15 K is −4407 kJ ⋅ kg−1.

5.5 Melting heat

Melting heat, within the experimental error of ±(0.5–1%), does not depend on the ortho-para composition. For n-Н2 at Т = 13.947 К and Р = 0.0072 MPa, melting heat ΔНmelt = 58.24 kJ kg−1.

Error of the calculated data is ±1 %. Data on the melting heat of parahydrogen at pressures up to 35 MPa can be described by the following equation:(31) ΔНmelt=58.23+8.702⋅10−7Ρ,kJ⋅kg−1(*),

where P — pressure, Pa.

The calculated data agree with the experimental data within the experimental error (approx. ±1 %).

Table 49 shows the values of the melting heat of parahydrogen, calculated by Eq. (31).Table 49 Melting heat of parahydrogen ΔНmelt, kJ. kg −1 [59].

Table 49P, MPa	0.0070	0.020	2.619	5.512	13.785	
T, K	13.80	13.81	14.65	15.53	17.81	
ΔНmelt	58.24	28.25	60.51	63.03	70.23	
P, MPa	20.506	20.678	27.916	34.257		
T, K	19.48	19.52	21.19	22.55		
ΔНmelt	76.07	76.22	82.52	88.04		

5.6 Evaporation heat [60]

Table 50 shows data on the evaporation heat of normal hydrogen and parahydrogen.Table 50 Evaporation heat of normal hydrogen and parahydrogen Δ Нev, kJ ⋅ kg−1.

Table 50T, K	ΔНev	T, K	ΔНev	T, K	ΔНev	
n-Н2	p-Н2	n-Н2	p-Н2	n-Н2	p-Н2	
14	457.84	450.40	22	445.44	437.50	30	303.57	291.17	
15	460.32	452.38	23	437.50	428.57	30.5	285.22	271.33	
16	461.81	453.87	24	427.08	418.65	31.5	213.79	220.73	
17	462.60	454.86	25	414.68	405.76	32.5	166.87	136.90	
18	461.81	453.87	26	399.80	390.38	32.98	–	0	
19	459.82	452.38	27	381.94	372.02	33	99.21	–	
20	456.84	448.91	28	360.61	349.70	33.23	0	–	
21	452.38	443.95	29	335.32	323.91		0	–	

The experimental data for n-H2 can be described by the following equation [60]:(32) ΔНev=456.3–0.56(Τ–16.6)2,kJ.kg−1

Near the normal boiling point, the error is ±1 %; near the triple point, it reaches ±4 %. At higher temperatures, the error can reach tens of percent.

Table 51 shows the dependence of evaporation heat on temperature.Table 51 Evaporation heat of liquid parahydrogen at saturation line ΔНev, kJ⋅.kg−1 [2].

Table 51T, K	13.8	14	15	16	17	18	19	20	
ΔНev	449.2	449.6	451.6	453.0	453.2	453.2	450.1	446.5	
T, K	20.268	22	24	26	28	30	32	32.976	
ΔНev	445.5	435.1	416.4	389.0	349.3	280.5	188.5	0	

5.7 Heat of combustion

According to work [61], the highest and lowest values of the heat of combustion are 143,105 kJ. kg−1 (12,779 kJ m−3) and 121,019 kJ kg−1 (10,760 kJ. m−3), respectively.

5.8 Heat of conversion

Table 52 shows the calculated data on the heat of conversion of hydrogen.Table 52 Calculated data on the heat of conversion of hydrogen ΔНconv, kJ ⋅ kg−1 [61].

Table 52T, K	о-Н2→ n-Н2	n-Н2 → Н2a	T, K	о-Н2→ n-Н2	n-Н2 → Н2a	T, K	о-Н2→ n-Н2	n-Н2 → Н2a	
0	–	525.19	40	703.29	444.92	120	570.04	–	
10	703.32	–	50	702.93	362.53	125	–	37.34	
15	–	525.10	60	701.18	–	150	430.27	15.08	
20	703.32	523.80	70	696.16	–	175	–	5.67	
20.39	703.32	–	75	–	184.32	200	218.48	2.06	
25	–	518.15	80	685.70	–	250	94.10	0.23	
30	703.32	503.84	90	668.12	–	273	–	0.14	
33.1	703.32	–	100	642.66	88.04	298.16	38.11	–	
a Equilibrium composition.

The error of calculating the heat of conversion is not specified.

5.9 Heat of adsorption

For hydrogen, the heat of adsorption is 628.0 J mol−1 [62].

6 Conclusion

Currently, hydrogen is considered a promising energy carrier that can provide reliable, affordable, steady and more environmentally friendly energy [63]. Most studies on hydrogen energy are related to hydrogen production (Table 53).Table 53 Top 10 promising hydrogen technologies.

Table 53

At this stage of the value chain, there is a significant diversity of technologies, although hydrogen storage is considered the most expensive, primarily due to its high explosiveness and fugacity. Currently, most national studies address the production of hydrogen fuel cells, which convert chemical energy into electricity and are used in industry for the autonomous generation and storage of energy, in transport (air, road, rail), in electric power engineering to supply power to remote and hard-to-reach areas. Another significant area of scientific research is the search and development of materials for hydrogen components.

The production of environmentally friendly “green” hydrogen, primarily through water electrolysis with the use of renewable energy sources, remains an expensive technology that can be implemented only in distant future. The current level of readiness is not sufficient for the commercialization of these developments. They have gained popularity due to consistent large-scale investments in research by a number of states. The cost of electrolizers is gradually decreasing (by half in 2018–2022), more powerful and scalable units are appearing, although their use is still limited.

As for the promising developments of hydrogen storage technologies, the main challenge now is to develop such commercial hydrogen storage systems that would be energy efficient and spacious. One of the most convenient and least expensive options for long-term use on an industrial scale is underground hydrogen storage.

The main constraints to the development of hydrogen energy sector are challenges of materials science and the need to improve technologies of hydrogen transportation, storage and consumption. Among the promising methods of hydrogen transportation, the following can be mentioned: by pipes, by road, sea, rail in compressed, liquefied or bound state, including as ammonia, in liquid or solid carriers. In this case, the main materials science challenge is the embrittlement of metals by hydrogen. The issue of hydrogen embrittlement is closely related to the cold resistance of structural materials. Researchers and engineers are seeking to develop modern hydrogen consumption systems, including turbine generators and engines. Besides, it is required to develop regulatory documentation on materials, technologies, and structures related to this topic.

A significant challenge in the widespread implementation of hydrogen energy lies in the need to build carbon storage facilities since hydrogen production must comply with carbon dioxide emission requirements. This causes the increased cost of hydrogen compared to conventional energy carriers. Therefore, it is necessary to develop technologies to reduce the cost of hydrogen production, transportation, storage and consumption.

Currently, the main focus is on alternative energy (wind and solar), which makes it possible to produce green hydrogen. It is hydrogen produced in industrial processes without releasing carbon dioxide into the atmosphere — carbon-free closed-cycle technology in water electrolysis. For example, a wind or solar farm generates electricity that is further used to electrolyze water. Molecular hydrogen and oxygen are produced. Oxygen is further utilized in a closed cycle, as is water that is produced in the combustion of hydrogen. It is necessary to introduce and improve technologies of green hydrogen production.

Some aspects of hydrogen use. Hydrogen allows the storage of electrical energy from renewable sources and ensures its stable supply. Hydrogen is also a more economical solution, especially when used for combustion in burners or internal combustion engines. Particularly effective are cogeneration units, which produce electricity and heat with high efficiency from the chemical energy of hydrogen. Hydrogen is also convenient for refueling vehicles, since it does not require a long charging time, unlike batteries, which create a large load on the local network. Hydrogen can be used for a wide range of projects in different areas of industry. For example, adding hydrogen to methane fuel is possible, but this requires caution in terms of burner adjustment and pipeline safety. It should also be taken into account that as the proportion of hydrogen in the mixture increases, its volumetric energy density decreases and more storage space is required.

The introduction of fuel cells can be accelerated by the wider use of dual-fuel internal combustion engines, which can run on hydrogen or on fossil or renewable liquid fuels. The transformation of the energy structure will be costly and is unlikely to be fully realized in the near future in developing countries, which are the main sources of greenhouse gases.

The situation may also be affected by the shortage of expensive catalysts used, unless a cheaper substitute for their active component is found, and the European campaign against fluorinated polymers. Therefore, for all proposed energy changes and in various engineering solutions, it is necessary to conduct a comprehensive analysis and assessment of the entire life cycle of hydrogen application without ideological bias.

In the case of hydrogen, it makes sense to develop different paths to renewable energy sources in order to compare their efficiency and impact. The ideological approach of “one right solution” is too risky and technically unjustified given the current level of uncertainty.

Directions of scientific research. Most national research today concerns the production of hydrogen fuel cells that convert chemical energy into electricity and are used in industry for autonomous generation and storage of energy, in transport (air, road, rail), in the electric power industry to provide energy to remote and hard-to-reach areas.

An equally important area of scientific research is the search for and creation of materials for hydrogen components. Only on the basis of special materials and compounds is it possible to effectively operate hydrogen-based energy generators. First of all, scientific interest concerns the development of materials used for catalysts that ensure the generation of electricity. Catalytic technologies, without which the entire modern oil refining and chemical industry, oil and gas chemistry, pharmaceutical and food industries are unthinkable, form the basis of hydrogen technologies. Accordingly, today the possibilities of using cheap materials for catalysts are actively studied.

Currently, the production of environmentally friendly “green” hydrogen, primarily through water electrolysis using renewable energy sources, remains an expensive technology with distant prospects for widespread implementation. The current level of readiness does not yet allow us to talk about the commercialization of these developments. They have gained popularity due to large-scale and systematic investments in research by a number of countries. The cost of electrolyzers is gradually decreasing (by half in 2018–2023), more powerful and scalable installations are appearing, although their use is still limited.

As for promising developments in hydrogen storage, today the main task is to create such commercial storage systems that would be distinguished by energy efficiency and capacity. One of the most convenient and least expensive options for long-term use on an industrial scale is underground hydrogen storage.

Innovative developments and scientific research today in the field of hydrogen consumption mainly concern the possibility of its use and scaling of projects within the framework of the development of automobile electric transport.

The most important physical and chemical properties of hydrogen addressed in the paper make it possible to choose technologies that will ensure the high efficiency of its practical use.

Ethics approval and consent to participate

Not applicable.

Consent for publication

All authors of the participants are informed and have provided consent for publication.

Funding

Not applicable.

Additional information

All authors participated in manuscript review and revision.

Data availability statement

No data was used for the research described in the article.

CRediT authorship contribution statement

A.A. Levikhin: Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. А.А. Boryaev: Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Formal analysis, Data curation, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

Not applicable.
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