If the heat required to increase the rms speed of 4 moles of a diatomic gas from $v$ to $\sqrt{3} v$ is 83.1 kJ , then the initial temperature of the gas is

(universal gas constant $=8.31 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ )

The length of a metal rod is 20 cm and its area of cross-section is $4 \mathrm{~cm}^2$. If one end of the rod is kept at a temperature of $100^{\circ} \mathrm{C}$ and the other end is kept in ice at $0^{\circ} \mathrm{C}$, then the mass of the ice melted in 7 minutes is (Thermal conductivity of the metal $=90 \mathrm{Wm}^{-1} \mathrm{~K}^{-1}$ and latent heat of fusion of ice $=336 \times 10^3 \mathrm{Jkg}^{-1}$ )

The heat required to convert 8 g of ice at a temperature of $-20^{\circ} \mathrm{C}$ to steam at $100^{\circ} \mathrm{C}$ is [specific heat capacity of ice $=2100 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$, specific heat capacity of water $=4200 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$, latent heat of fusion of ice $=336 \times 10^3 \mathrm{~J} \mathrm{~kg}^{-1}$ and latent heat of steam $\left.=2.268 \times 10^6 \mathrm{Jkg}^{-1}\right]$

Two moles of a gas at a temperature of $327^{\circ} \mathrm{C}$ expands adiabatically such that its volume increases by $700 \%$. If the ratio of the specific heat capacities of the gas is $\frac{4}{3}$, then the work done by the gas is (Universal gas constant $=8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ )