A diatomic gas $\left(\gamma=\frac{7}{5}\right)$ is compressed adiabatically to volume $\frac{\mathrm{V}_0}{32}$, where $\mathrm{V}_0$ is its initial volume. The initial temperature of the gas is $\mathrm{T}_{\mathrm{i}}$ in kelvin and the final temperature is $\mathrm{xT}_{\mathrm{i}}$ in kelvin. The value of $x$ is

The work done by a gas as it is taken in a cyclic process (shown in graph) is

Two gases A and B are at absolute temperatures 350 K and 420 K respectively. The ratio of average kinetic energy of the molecules of gas $B$ to that of gas A is

A composite slab consists of two materials having coefficients of thermal conductivity K and $2 K$, thickness $x$ and $4 x$ respectively. The temperatures of two outer surfaces of a composite slab are $\mathrm{T}_2$ and $\mathrm{T}_1$ respectively $\left(\mathrm{T}_2>\mathrm{T}_1\right)$. The rate of heat transfer through the slab in a steady state is $\left[\frac{A\left(T_2-T_1\right) K}{x}\right] f$, where $f$ is equal to