Assuming that hydrogen gas behaves as an ideal gas under these conditions, the ideal gas law is a good starting point for this calculation. It relates the pressure, volume, and temperature of a gas to the number of molecules it contains. The ideal gas law is usually stated as:

PV = nRT

where P is the pressure, V is the volume, n is the number of moles, R is the ideal, or universal, gas constant, and T is the absolute temperature (in Kelvin).

Here, we want to find the mass of hydrogen gas (H2), so we'll need to convert from moles to grams using the molar mass of hydrogen gas.

First, let's convert the given values into SI units so we can use R=8.3145J/(mol.K):

• Pressure P: 17.5 bar = 1750000 Pa (since 1 bar = 100000 Pa),
• Volume V: 6 liters = 0.006 m³ (since 1 liter = 0.001 m³),
• Temperature T: 25 degrees Celsius = 298.15 K (since T(K) = T(C) + 273.15),
• Ideal gas constant R: 8.3145 J/(mol·K).

We can rearrange the ideal gas law to solve for n (the number of moles):n = PV/RT

Substituting the given values:

n = (1750000 Pa * 0.006 m³) / (8.3145 J/(mol·K) * 298.15 K) ≈ 4.24 mol.

The molar mass of H2 is approximately 2 g/mol (2.016 g/mol), so the mass m of the hydrogen gas is:m = n * molar mass. Substituting the valuesm = 4.24 mol * 2 g/mol

Using Enthalpy:

The energy released in the combustion of hydrogen is given by its heat of combustion. The heat of combustion (also known as the enthalpy of combustion) of hydrogen is about -286 kJ/mol. This value is negative because energy is released (exothermic process) during the combustion.

The heat of combustion (ΔH) is typically given per mole of substance combusted. So, to find the total energy released (E), we multiply the heat of combustion by the number of moles: E = -ΔH * n

We have around 4.24 moles of hydrogen in 6L at 25C and 17.5bars. Substituting the values:

E = -(-286 kJ/mol) * 4.24 mol

After doing the calculation, we find that E ≈ 1212.64 kJ.

Energy values can be converted from kilojoules (kJ) to kilowatt-hours (kWh) using the following conversion factor (1 kWh = 3600 kJ), so, to convert the energy released E (which we have found to be approximately 1212.64 kJ) to kWh, we divide by 3600: E_kWh = 1212.64 kJ / 3600

So, assuming perfect combustion, approximately 1.2MJ (0.337 kWh) of energy can be released by this quantity of hydrogen. Please note that this calculation assumes a perfect combustion process, which may not be completely accurate in the real world due to factors such as heat loss to the surroundings.

Using heat value in J/kg:

The energy content of hydrogen per kilogram is 33.33 kWh/kg or 120kJ/kg

Therefore if m=8.48g, the energy is ≈ 33.33kWh/kg*8.48/1000kg = 0.283kWh

Using volumetric energy density: ….it depends on the pressure. The values in (C) are for LIQUID hydrogen, so we cannot use this method here.

Notes:

• These canisters should resist more pressure: they are tested and should sustain at least 34bars. At that pressure we need about 23 canisters… but obviously this is not safe.
• However, it is interesting to note that the output of the H2 electrolyser is about 35 bars. This means that LPG canisters are almost good, but at their limit (no margin of security).
• Other pressurized tanks can work though, like a scuba tank (see on the right). Assuming a typical tank (see on the right), having a usable volume of 11.1L and resisting well over 35bars (up to 232bars!), the number of tanks needed will be equal to:

107.5 * 17.5/232 * 6/11.1 = 4.38 scuba tanks (@232bars, from a typical scuba tank compressor.)

…or if using the pressurized hydrogen coming from the electrolyser (35bars):

107.5 * 17.5/35 * 6/11.1 = 29 scuba tanks (@35bars).

Note that this pressure is right at the limit of what the “3kg LPG” canister can withstand). Interestingly, the electrolytic cell we have can produce 15L of compressed hydrogen at 35 bar. That is about one and a half scuba tanks per day. In two days, the energy for the month can be produced and stored.

Typical scuba tank:

1. Size (Volume): The volume of the most commonly used scuba tank for recreational diving is typically around 11.1 liters (or 0.0111 cubic meters). This is the so-called "Aluminum 80" tank, with "80" referring to its capacity in cubic feet under normal atmospheric pressure. It's important to note that this is not the physical volume of the tank, but the volume of air it can hold at atmospheric pressure.
2. Pressure: Scuba tanks are also rated for a specific maximum pressure. The Aluminum 80 tanks are typically rated for a maximum pressure of about 200 bar or 20,000 kPa (kilopascal). High-pressure steel tanks can have a maximum pressure of up to 232 bar or 23,200 kPa, or even higher.
3. Physical Dimensions: The physical dimensions of an Aluminum 80 scuba tank are typically about 66 cm in height and about 18.4 cm in diameter

A) Energy in a 6L (25C) canister depending on it’s content

B) Quantity H2 canisters/balloons to substitute one LPG canister (6L at 25C) at different pressures:

Reminder: LPG canister has 33.15 kWh of energy, equivalent to 33.15/33.33kg of hydrogen, or about 1kg of H2 (995 grams).

(*) Natural Gas is mostly methane. Methane has a slightly higher energy density than propane (and LPG is made of propane and methane mostly). Gravimetric energy density of Methane is ~ 55.5MJ/kg.

From a quick calculation using PV=nRT at ambient pressure (1atm) and temperature (25C), and considering that the mass of methane needed to produce the same usable energy in an LPG 3kg canister is 116MJ is equal to 116/55.5 = 2.09kg, and the molar mass of methane is approximately 16.04 g/mol (12.01 g/mol for carbon and 4.03 g/mol for hydrogen), corresponding to n = 2090g/16.04g = 130.3 moles:

V = nRT/P = 130.3 mol*0.0821 L·atm/(K·mol) * 298.15 K / 1atm = 3189 Liters (note Avogadro constant in LITERS.atm/(K.mol))

Another way using energy density (volumetric):

• At standard pressure/temperature, Natural Gas has an energy density of 0,0364MJ/L (reminder: gaseous H2 energy density is

Reminder:

• Liquid LPG: 116MJ or 32.25kWh of energy in one “3kg LPG canister”
• Liquid H2:

Energy released by chemical reactions (oxidation):

• In the USA, hydrogen costs around US$16 per kilogram. Currently, renewable hydrogen produced via electrolysis costs between US$3 – US$6/kg, though analysts expect this figure to drop significantly over the next decade (from here)
• The 3 kg LPG is subsidized by the government, with the price set by each local government. Prices are officially set at IDR 16.000 per canister in Java island (from here)
• From Gender and Fossil Fuel Subsidy Reform: An audit of data on energy subsidies, energy use and gender in Indonesia, Nov. 1, 2017, pp. 9-19:
💡

1 LPG canister At 2.4 bars: ↔ 288 H2 manually compressed canisters, or about 4 cubic meters of H2 at ambient temperature At 17.5 bars:

Note: A volume of around 11 m3 (which is the volume of the trunk of a large utility or commercial vehicle) is needed to store just 1 kg of hydrogen, which is the quantity needed to drive 100 km.