Let us consider one-gram molecule (mole) of the gas. Let M and V be its mass and volume respectively. The pressure exerted by the gas is given by:
But PV = RT
where T is the absolute temperature of the gas and R is the molar gas constant. R is the gas constant for 1-gram molecule of the gas.
[The value of R is 8.315 J mol-1 K-1 or 8.315x107 mol-1 K-1 or 1.985 cal mol-1 K-1]
The average translational kinetic energy per gram molecule of the gas is equal to 
RT.
Note : The average translational kinetic energy per garm of gas is
(3/2)(R/M) T. Here, M is the molecular weight of the gas.
Dividing both sides of equation (1) by N, where [N is the Avogadro's number] we get
The average translational kinetic energy per molecule is equal to kT.
It is clear from equation (2) that the mean kinetic energy of a molecule is directly proportional to the Kelvin (or absolute) temperature of a gas. When the temperature of the gas is increased, the mean kinetic energy of the molecules increases. On the other hand, when heat is withdrawn from a gas, the mean kinetic energy of the molecules decreases. Thus, the temperature of a gas is a measure of the mean translational kinetic energy per molecule of the gas. This is also known as 'kinetic interpretation of temperature'.
Absolute zero of temperature
when T = 0, then C = 0
This leads us to the following definition of 'absolute zero of temperature'.Absolute zero of temperature may be defined as that temperature at which the rms velocities of the gas molecules become zero. In other words, all molecular motion ceases at absolute zero of temperature.
The value of absolute zero for an ideal gas is -273oC.The definition is true only in the case of an ideal gas. The gases used in actual practice are far from being ideal, particularly at extremely low temperatures. Before the absolute zero of temperature is reached, all the gases change their state to liquids and then to solids.
