From the following statements concerning ideal gas at any given temperature T, select the correct one (s)

Options

A. The coefficient of volume expansion at constant pressure is the same for all ideal gases.
B. The average translational kinetic energy per molecule of oxygen gas is `3kT`, k being the Boltzmann constant.
C. The mean free path of molecules increases with decrease in pressure.
D. In a gaseous mixture, the average translational kinetic energy of the molecules of each component is different.

Answer

A, C

Explanation

For `1` mole of an ideal gas
`pV=RT` (i)
at constant pressure:
`PdV=RdT`
From Eqs. (i) and (ii), we get (ii)
`(dV)/(V)=(dT)/(T)`
The coefficient of volume expansion at constant pressure is given by
`(dV)/(VdT)=(1)/(T)`
same for all gases at same temperature.
The average translational kinetic energy per molecule is `(3//2)kT` and not `3kT` . With decrease in pressure, volume of the gas increases so its mean free path increases. [Option `(c)`]
The average translational kinetic energy of the molecules is independent of their nature, so each component of the gasesous mixture will have the some value of average translational kinetic energy.