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EXPLAIN KINETIC INTERPRETATION OF TEMPERATURE

A hotter body has greater internal energy than a similar colder body. Thus, higher temperature means higher internal energy and lower temperature means lower internal energy. According to the kinetic theory of gases, the internal energy of an ideal gas is the same as the total translational kinetic energy of its molecules, which is, from equation (vii),

 for a given sample of a gas, higher temperature means higher value of v_rms and lower temperature means lower value of v_rms. 

for a given sample of a gas.Let p and v be the pressure of the gas and the rms speed of the molecules at temperature T, respectively. Let p_tr and v_tr be the values of these quantities at temperature 273.16 K, keeping the volume V the same as that at T.

From equation (v),

From the definition of absolute temperature scale,

From (viii) and (ix),

Now, v_tr is the rms speed of the molecules at 273.16 K and hence, is constant for a given gas. Equation (x) shows that the absolute temperature of a given gas is proportional to the square of the rms speed of its molecules. As the total translational kinetic energy of the molecules is K.E  we see that T µ K. E for a given sample of a gas.

Thus, the absolute temperature of a given sample of a gas is proportional to the total translational kinetic energy of its molecules.

Now consider a mixture of two gases A and B. Let m₁ be the mass of a molecule of the first gas and m₂, be that of the second. As the molecules collide with each other, they exchange energy. On an average, the molecules with higher kinetic energy lose energy at equilibrium, the average kinetic energy of all molecules are equal.

We find that for different kinds of gases, it is not the rms speed, but average kinetic energy of individual molecules that has a fixed value at a given temperature. The heavier molecules move with lower rms speed and the lighter molecules move with higher rms speed.