Useful Equations

It can be hard to track the various measures used for hydrogen systems. Below are some conversions and definitions:

STP = standard temperature/pressure = 0°C (32°f) and 1 bar (≈1 atmosphere).But: Some references say STP is 25°C (77°f). We do not understand this discrepancy.

NTP = normal temperature/pressure = 20°C (68°f) and 1 atm (atmosphere). Functionally, NTP is almost the same as STP , and STP is more common.

1 atm = 1 atmosphere = 14.7 psi.

scf = “scuff” = standard cubic foot = 1 c.f. (STP).

ncf = normal cubic foot = 1 c.f. (NTP).

1 gallon = 3.78 liters

1 cubic foot = 7.5 gallons = 28.25 liters.

1 liter = 1000 cc (cubic centimeters).

1 kilogram = 1kg = 1000 grams.

The Ideal Gas Law:                  Pressure x Volume       =   PV  =  constant.                                             no. of atoms x Temperature      nT In practice we have temperature and volume both constant. “No. of atoms” is equivalent to “amount of gas”. The Gas Law says that for fixed volume, if we double (or triple etc) the pressure we double (or triple etc) the amount of gas. This is an awesome result. For example, a 60 cubic foot tank filled to 200 psi (14 atm) contains about 60 x 14 = 840 scf of gas.This equality is accurate for hydrogen (and most gases) to within 2% up to 30 atm (≈450 psi). Even at higher pressures, say 3000 psi, the Gas Law is accurate to within 15-20% for hydrogen (it predicts a bit low). Temperature is in degrees Kelvin, so it’s effectively constant: Because 0° C = 273° K, and 20° C = 293° K, the ratio of two real-life Kelvin temperatures is always close to 1, and thus does not affect the equation.

A K-cylinder holds about 1 cubic foot. The scf it holds will vary with the gas and the company. A K-cylinder of hydrogen (at 2500 psi) holds roughly 200 scf. A K-cylinder of nitrogen (at 3000 psi) holds roughly 250 scf. (Note that these figures are higher than the Gas Law predicts.)

mole is a certain amount of stuff, defined as 6 x 1023 molecules of the compound (Avagadro’s number). The mass of 1 mole of a compound is equal to its atomic weight, in grams. For example, 1 mole of water (H2O) has 2 x 1 + 16 = 18 grams mass.

Avagadro’s Law: The volume of 1 mole of any gas (stp) = 22.4 liters. This is an amazing, useful result.

Mass of 1 mole hydrogen gas (H2) = 2 grams. So the mass of 22.4 liters (stp) H2 is 2 g.Mass of 1 mole nitrogen gas (N2) =28 g.Mass of 1 mole oxygen gas (O2) = 32 g.Mass of 1 mole air ≈ 29 g.Mass of 1 mole propane (C3H8) = 44 g.Mass of 1 mole natural gas (mostly methane, CH4) ≈ 16 g.Mass of 1 mole gasoline (C8H18) = 114 g.

Air ≈ 78% nitrogen, 21% oxygen, 1% other (argon, particulates,,water vapor), 0.03% CO2(!).

Avagadro’s Law also implies that for gases at equal pressure and temperature, proportions of volume are the same as proportions of amount of gas. For example, 1 cc of H2 mixed with 1 liter of air gives a 0.1%, or 1000 ppm, concentration of H2.


Amps x Volts = Watts. For example, a 100 watt bulb draws 0.83 amps at 120 volts.

Joule, Watt-hour, Btu and calorie are all units of energy. Watt-hours are the most convenient unit for electric systems.

1 Watt = 1 Joule/second. So 1 Watt-hour = 3.6 kJ. This is the most relevant conversion.

1 kW = 1 kilowatt = 1000 watts.

1 Btu ≈ 1 kJ = 1 kiloJoule = 1000 J.

1 calorie = 4.184 J.     (Aside: A “calorie” as used for food energy is actually a kilocalorie, or 1000 calories, so an english muffin contains 130,000 calories, = 130 “calories”.)

Energy storage of a lead-acid L-16 battery: 350 amp-hours @ 6 volts =2100 Wh. nominal. Effective (usable) energy is half, ie about 1 kWh. The usable storage is less because draining batteries beyond about half shortens their lifespan drastically.

Energy Density of H(STP) = 3.2 – 3.5 Watt-hours/liter. The figure can be calculated different ways (in particular,assuming different temperatures), giving different results.Energy released by combustion of H2 = 242 kJ/mole. This is the energy released in the reaction H2 + ½ O2 → H2O (steam) + heat. In a fuel cell, part of this energy is electrical, part is heat. Compare natural gas (800 kJ/mole) and gasoline (5500 kJ/mole).Per kilogram, H2 stores more energy because a mole of H2 weighs so much less. But 242 kJ of H2 takes up the same volume (= 22.4 liters, stp) as 800 kJ of natural gas. Gasoline, because it is a liquid, is much more dense- 22.4 liters of gasoline is roughly 160 moles, containing 900,000 kJ of energy! It is more energy-dense than dynamite. One can readily see why our civilization has become so dependent on oil- it is miraculous stuff. But hydrogen is miraculous too, in different ways.