Question

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

I. At constant pressure the value of $\frac{1}{n} \frac{dV}{dT}$ is same for all ideal gases.

II. The average translational kinetic energy per molecule of oxygen gas is 3 KT(K being Boltzmann constant).

III. In a gaseous mixture, the average translational kinetic energy for each component of gas is always same.

IV. The mean free path of molecules increases with decrease in pressure keeping temperature constant.

• A. II and III
• B. 1 only
• C. I and II
• D. II and III

Answer 1

I, III, and IV are correct. None of the provided options are correct.

Answer 2

For an ideal gas:

• (I) Since $PV=nRT$, at constant pressure $V=\frac{nRT}{P}$. Differentiating, $\frac{dV}{dT}=\frac{nR}{P}$ so that

  $$\frac{1}{n}\frac{dV}{dT}=\frac{R}{P},$$

  which is independent of the gas. Hence, statement (I) is true.

• (II) The average translational kinetic energy per molecule is

  $$\frac{3}{2} kT,$$

  not $3kT$. So (II) is false.

• (III) In a mixture at thermal equilibrium, every component is at the same temperature; thus each molecule (regardless of type) has an average translational kinetic energy $\frac{3}{2}kT$. So (III) is true.

• (IV) The mean free path $\lambda$ varies inversely with pressure. A decrease in pressure reduces the number of collisions, increasing $\lambda$. Therefore, (IV) is true.