FLUID MECHANICS | Gas Laws

The Ideal Gas Law relates pressure, volume, molecular quantity, and temperature of an ideal gas
together in one neat mathematical expression:
PV = nRT
Where,
P = Absolute pressure (atmospheres)
V = Volume (liters)
n = Gas quantity (moles)
R = Universal gas constant (0.0821 L · atm / mol · K)
T = Absolute temperature (K)
An alternative form of the Ideal Gas Law uses the number of actual gas molecules (N) instead
of the number of moles of molecules (n):
PV = NkT
Where,
P = Absolute pressure (atmospheres)
V = Volume (liters)
N = Gas quantity (moles)
k = Boltzmann’s constant (1.38 × 10−23 J / K)
T = Absolute temperature (K)
Although no gas in real life is ideal, the Ideal Gas Law is a close approximation for conditions of
modest gas density, and no phase changes (gas turning into liquid or visa-versa).
Since the molecular quantity of an enclosed gas is constant, and the universal gas constant must
be constant, the Ideal Gas Law may be written as a proportionality instead of an equation:
PV ∝ T
Several “gas laws” are derived from this Ideal Gas Law. They are as follows:
PV = Constant Boyle’s Law (assuming constant temperature T)
V ∝ T Charles’s Law (assuming constant pressure P)
P ∝ T Gay-Lussac’s Law (assuming constant volume V )
You will see these laws referenced in explanations where the specified quantity is constant (or
very nearly constant).

For non-ideal conditions, the “Real” Gas Law formula incorporates a corrected term for the
compressibility of the gas:
PV = ZnRT
Where,
P = Absolute pressure (atmospheres)
V = Volume (liters)
Z = Gas compressibility factor (unitless)
n = Gas quantity (moles)
R = Universal gas constant (0.0821 L · atm / mol · K)
T = Absolute temperature (K)
The compressibility factor for an ideal gas is unity (Z = 1), making the Ideal Gas Law a limiting
case of the Real Gas Law. Real gases have compressibility factors less than unity (< 1). What this
means is real gases tend to compress more than the Ideal Gas Law would predict (i.e. occupies less
volume for a given amount of pressure than predicted, and/or exerts less pressure for a given volume
than predicted).