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 3 kT, k being Boltzmann constant
• C. The mean-free path of molecules increases with decrease 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)

For one mole of an ideal gas
$pV=RT$
The coefficient of volume expansion at constant pressure is given by
$\left(\frac{\Delta V}{\Delta T}\right)_{v}=\frac{R}{p} $ = constant [option (a)]
The average translational kinetic energy per molecule is $(3/2)kT$ and not $3\, kT$. With decrease of pressure, volume of the gas increases so its mean free path, [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