An ideal gas is made of polyatomic molecules. Each of the molecules has three translational, three rotational and $f$ number of vibrational modes. If the ratio of heat capacities $C_P / C_V$ of the gas is $8 / 7$, then the value of $f$ is:

The mean free path of molecules in an ideal gas $A$ is half that of another ideal gas $B$. The diameter of the spherical molecules of gas $A$ is twice the diameter of the molecules of $B$. If number densities of the gases $A$ and $B$ are $n_A$ and $n_B$, respectively, the correct option is:

One mole of an ideal monatomic gas undergoes a cyclic process as shown in the figure. The total heat supplied to the gas is:

A flask contains argon and chlorine in the ratio of $2: 1$ by mass. The temperature of the mixture is $27^{\circ} \mathrm{C}$. The ratio of root mean square speed of the molecules of the two gases $\left(\frac{V_{\mathrm{rms}}^{\mathrm{Ar}}}{V_{\mathrm{rms}}^{\mathrm{Cl}}}\right)$ is:

(Atomic mass of argon $=40.0 \mathrm{u}$ and molecular mass of chlorine $=70.0 \mathrm{u}$ )