Find the mass of oxygen gas with which $1.882 \times 10^{23}$ degrees of freedom are associated at N.T.P. Given: Molar mass of diatomic gas, oxygen is $32 \mathrm{~g} \mathrm{~mol}^{-1}$ and oxygen molecule possess three translational and two rotational degrees of freedom.

Two bodies of specific heats $C_1$ and $C_2$, having the same heat capacities are combined to form a single composite body. The specific heat capacity of the composite body is

1 kg of water at $100^{\circ} \mathrm{C}$ is converted to steam at the same temperature. Volume of 1 cc of water changes to $1671 \times 10^3 \mathrm{cc}$ on boiling. The change in internal energy of the system is (Latent Heat of vaporisation of water is $22.68 \times 10^5 \mathrm{~J} \mathrm{~kg}^{-1} ; 1 \mathrm{~atm}=1.0 \times 10^5 \mathrm{~Pa}$ )

An ideal gas has molar specific heat $\frac{5 R}{2}$ at constant pressure. If 1662 J of heat brings about 50 K temperature change, the number of moles of gas is