Question

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

• 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 Boltzmann constant
• C. The mean-free path of molecules increases with increase in the pressure
• D. In a gaseous mixture, the average translational kinetic energy of the molecules of each component is different

Answer 1

Answer: (A), (C)

The correct options are
A The coefficient of volume expansion at constant pressure is the same for all ideal gases
C The mean-free path of molecules increases with increase in the pressure

• For $1$ mole of an ideal gas
  

$pV=RT...\left(i\right)$
at constant pressure:
$PdV=RdT....\left(ii\right)$
From Eqs. (i) and (ii), we get
$\frac{dV}{V}=\frac{dT}{T}$
The coefficient of volume expansion at constant pressure is given by
$\frac{dV}{VdT}=\frac{1}{T}$
same for all gases at same temperature.

• The average translational kinetic energy per molecule is $\left(3/2\right)kT$ and not $3kT$.
• With decrease in pressure, volume of the gas increase 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 gaseous mixture will have the same value of average translational kinetic energy.