Classification of Gases: Real Gases and Ideal Gases

A gas whose molecules are identical, spherical, rigid, and perfectly elastic point masses, which keep colliding among themselves and with the walls of the containing vessel in perfectly elastic collisions (total energy before collision = total energy after collision), and between which no attractive or repulsive force acts, is called an ideal gas.

The equation that combines Boyle's Law, Charles' Law, and Gay-Lussac's Law into a single relation for a fixed mass of gas, relating the quantities pressure (P), volume (V), and temperature (T) which describe the state of the gas, is called the Equation of State.

Combining the above three laws for a fixed mass of gas:

PV = nRT

PV = N_kB​T

where:

• P = pressure, V = volume, T = temperature
• n = number of moles, R = universal gas constant
• N = number of molecules, k_B = Boltzmann's constant

At constant temperature, the volume of a fixed mass of gas is inversely proportional to its pressure.

V ∝ \[\frac {1}{P}\]

At constant pressure, the volume of a fixed mass of gas is directly proportional to its temperature.

V ∝ T(at constant P)

At constant volume, the pressure of a fixed mass of gas is directly proportional to its temperature.

P ∝ T(at constant V)