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Fluids

Ideal gas law


The properties of gases are in general well understood by the relation

PV = NkT = nRT


The symbol P represents the absolute pressure, V the volume, T the temperature and N is the number of particles in the gas.
 k represents the Boltzmann constant (1.38×10-23 JK-1).
 n is the amount of gas expressed in moles.
 R represents the ideal, or universal, gas constant (8.314 JK-1mol-1).

One has the following relations for N, n, k, R and Avogadro's number NA (6.02×1023 mol-1).

N = n NA     and     R = k NA


Notice that the relation expressed by the ideal gas law does not refer to the mass of the gas molecules.

At room temperature (T=293 K) and at a standard pressure of 1 atm (101325 Pa), one finds for the volume of 1 mol of a gas

V = nRT/P =
= (1 mol)×(8.314 JK-1mol-1)×(293 K)/(101325 Nm-2) = 0.024 m3


independent of the type of gas!

When at constant temperature T the volume of a gas is changed from V1 to V2, then its pressure change, from P1 to P2, is determined by

P2 = (V1/V2) P1     (Boyle, 1662)


When at constant volume V the temperature of a gas is changed from T1 to T2, then its pressure change, from P1 to P2, is determined by

P2 = (T2/T1) P1     ( Amontons, ~1700)


When at constant pressure p the temperature of a gas is changed from T1 to T2, then its volume change, from V1 to V2, is determined by

V2 = (T1/T2) V1     ( Charles, ~1780)


Boyle's law