Kinetic Molecular Theory Of Gases

Ratio of remains constant.
Average speed is the arithmetic mean of the speeds of molecules in a gas at a given temperature,
i.e.,
and according to kinetic theory of gases,
... (i)
Also, rms speed (root mean square speed)
is defined as the square root of mean of squares of the speed of different molecules, i.e.,

and according to kinetic theory of gases,
... (ii)
From Eqs. (i) and (ii), we get

(iii)
Therefore, constant
Hence, root mean square velocity is also become times.

Ideal gas equation is given by

For oxygen,
Therefore equation (i) becomes


For nitrogen


For mixture of gas

Here,

increase in

Let ' ' be the degree of freedom



gas must be monoatomic.

The internal energy for 1 mole of gas is given as
where is degrees of freedom


and