Thermodynamics & Heat Transfer · The ideal gas
The equation of state
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The equation of state

The gas laws compare two states of the same gas. The equation of state describes ONE state completely, and needs nothing to compare it to: PV=nRTPV = nRT, read aloud P V equals n R T.

Every letter, in words. PP is the absolute pressure in pascals. VV is the volume in cubic metres. nn is the amount of gas in moles — a count of molecules, six hundred billion trillion to the mole. TT is the absolute temperature in kelvin. And RR is the universal gas constant, 8.314 J/(mol·K): the exchange rate between energy and mole-kelvins, and universal in the strong sense — the same number for helium, for steam, for the air in this room.

Because RR is quoted in joules, it sets the units for everything else. Pascals, not kilopascals. Cubic metres, not litres. Kelvin, always. Feed it kPa and your answer is out by a thousand, in a direction that looks perfectly reasonable on the page. Rearranged: n=PVRTn = \dfrac{PV}{RT}, V=nRTPV = \dfrac{nRT}{P}, T=PVnRT = \dfrac{PV}{nR}.

Trade the moles for kilograms and you get a density. ρ=PMRT\rho = \dfrac{PM}{RT}rho equals P M over R T, with ρ\rho the Greek letter rho. ρ\rho is the density in kg/m³ and MM is the molar mass in kg/mol — which matters, because every data sheet in the world prints molar mass in GRAMS per mole. Air's 28.97 g/mol is 0.02897 kg/mol, and that one factor of a thousand is the whole lesson of this relation.