A gas is taken from state A to state B along two different paths 1 and 2. The heat absorbed and work done by the system along these two paths are $Q_1$ and $Q_2$ and $W_1$ and $W_2$ respectively. Then

At $27^{\circ} \mathrm{C}$ temperature, the mean kinetic energy of the atoms of an ideal gas is $\mathrm{E}_1$. If the temperature is increased to $327^{\circ} \mathrm{C}$, then the mean kinetic energy of the atoms will be

The ratio of molar specific heats of oxygen is

A solid cube of mass $m$ at a temperature $\theta_0$ is heated at a constant rate. It becomes liquid at temperature $\theta_1$ and vapour at temperature $\theta_2$. Let $s_1$ and $s_2$ be specific heats in its solid and liquid states respectively. If $L_f$ and $L_v$ are latent heats of fusion and vaporisation respectively, then the minimum heat energy supplied to the cube until it vaporises is