Density of gases: by pressure and temperature?

The density of gases matters in turbines, compressors, for energy transport and energy storage. Hence this data-file models the density of gases from first principles, using the Ideal Gas Equations and the Clausius-Clapeyron Equation. High energy density is shown for methane, less so for hydrogen and ammonia. CO2, nitrogen, argon and water are also captured.

The Ideal Gas Law states that PV = nRT, where P is pressure in Pascals, V is volume in m3, n is the number of mols, R is the Universal Gas Constant (in J/mol-K) and T is absolute temperature in Kelvin.

The Density of a Gas can be calculated as a function of pressure and temperature, simply by re-arranging the Ideal Gas Law, where Density ρ = P x Molecular Weight / RT. Our favored units are in kg/m3.

Density of methane in kg/m3 and kWh/m3

The Density of Methane (natural gas) can thus be derived from first principles in the chart below, using a molar mass of 16 g/mol, and then flexing the temperature and pressure. This shows how methane at 1 bar of pressure and 20ºC has a density of 0.67 kg/m3. LNG at -163ºC is 625x denser at 422 kg/m3. And CNG at 200-bar has a density of 180kg/m3.

Density of gases
Density of methane, LNG and CNG according to pressure and temperature

The Energy Density of Methane can thus be calculated by multiplying the density (in kg/m3) by the enthalpy of combustion in kJ/kg, and then juggling the energy units. A nice round number: the primary energy density of methane is 10 kWh/m3 at 1-bar and 20ºC, increasing with compression and liquefaction. CNG at 200-300 bar has around 30-60% of the energy density of gasoline, in kWh/m3 terms.

The energy density of methane is 10kWh/m3 as a nice rounded rule-of-thumb.

Clausius-Clapeyron: gas liquefaction?

Methane liquefies into LNG at -162ºC under 1-bar of pressure. The boiling points of other gases range from water at 100ºC, ammonia at -33ºC, CO2 at -78ºC, argon at -186ºC, nitrogen at -196ºC to hydrogen at -259ºC. This is all at 1-bar of pressure.

However, liquefaction temperatures rise with pressure, as can be derived from the Clausius-Clapeyron equation, and shown in the chart below. At 10-20 bar of pressure, you can liquefy methane into ‘pressurized LNG’ at just -105 – 123ºC, which can sometimes improve the efficiency of LNG transport. This can also help cryogenic air separation.

Density of gases
Boiling Points of Different Gases According to the Clausius Clapeyron Relationship

Density of CO2: strange properties?

The Density of CO2 is 1.87 kg/m3 at 20ºC and 1-bar of pressure, which is 45% denser than air (chart below). But CO2 is a strange gas. It cannot exist as a liquid below 5.2 bar of pressure, sublimating directly to a solid. CO2 can also be liquefied purely by compression, with a boiling point of 20-80ºC at 30-100 bar of pressure.

Density of Gas
Density of CO2 according to pressure and temperature in kg per m3

Hence often the disposal pipeline in a CCS or blue hydrogen value chain may often be pumping a liquid, rather than flowing a gas. And finally, these properties of CO2 open the door to surprisingly low cost CO2 transport by truck or in ships. This is all just physics.

Super-critical fluids: fourth state of matter?

There is also a fourth density state for all of the gases in the data-file. Above their critical temperature and critical pressure, fluids ‘become super-critical’. Sometimes this is described as ‘having properties like both a gas and liquid’. Mathematically, it means density starts rising more rapidly than would be predicted by the Ideal Gas Equations.

Super-critical gases behave unpredictably. Their thermodynamic parameters cannot be derived from simple formulae, but rather need to be read from data-tables and/or tested experimentally. This is why the engineering of supercritical systems tends to involve supercomputers.

Examples of super-critical gases? Steam becomes supercritical above 218-bar and 374ºC. CO2 becomes supercritical about 73-bar and 32ºC. Thus CO2 power cycles inevitably endure supercriticality.

Energy density of hydrogen lags other fuels?

The Density of Hydrogen is 0.08 kg/m3 at 20ºC and 1-bar of pressure, which is very low, mainly because of H2’s low molar mass of just 2g/mol. Methane, for example, is 8x denser. CO2 is 20x denser. In energy terms, gasoline is 3,000x denser per m3.

Hence hydrogen transportation and storage requires demanding compression or liquefaction. Tanks of a hydrogen vehicle might have a very high pressure of 700-bar, to reach a 40kg/m3 (the same density can be achieved by compressing methane to just 50-bar!). Liquefied hydrogen has a density around 70kg/m3 (LNG is 6x denser).

The density of hydrogen is just 0.08 kg/m3 at 20ºC of temperature and 1-bar of pressure

The energy density of hydrogen, in kWh/m3 also follows from these equations. At 1-bar and 20ºC, methane contains 3x more energy per m3 than hydrogen. Under cryogenic conditions, it contains 2x more energy. Under super-critical and ultra-compressed conditions, it contains 4x more.

The energy density of hydrogen is 50-75% lower than natural gas, even after compression/liquefaction

Data into the energy density of gases?

Similar energy density challenges constrain the use of ammonia as a fuel, as tabulated in the data-file, contrasted with other fuels, and discussed in our research note here.

This data-file allows density charts — in kg/m3 and in kWh/m3 — to be calculated for any gas, using the Ideal Gas Laws and the Clausius-Clapeyron equations. The data-file currently includes methane, CO2, nitrogen, ammonia, argon, water and hydrogen.

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