Assertion (A) Heat and work are modes of energy transfer to a system resulting in change in its internal energy.

Reason (R) Heat and work in thermodynamics are state variables.

The correct option among the following is

An ideal gas at pressure $p_0$ undergoes an isothermal expansion until its volume is 8.0 times its initial volume. The gas is slowly and adiabatically compressed back to its original volume. If the adiabatic constant of the gas is $\gamma=\frac{4}{3}$, then the ratio of the average kinetic energy per molecule in this final state to that, in the initial state is

At what temperature is the root mean square rms speed of neon gas atoms is equal to the rms speed of helium gas atoms at $-33^{\circ} \mathrm{C}$ ?

(Atomic mass of $\mathrm{Ne}=20.2 \mathrm{u}$, and that of $\mathrm{He}=4.0 \mathrm{u}$ )

A piece of metal has a weight of 49 g in air and 39 g in a liquid of density $1.2 \times 10^3 \mathrm{~kg} / \mathrm{m}^3 \mathrm{kept}$ at $32^{\circ} \mathrm{C}$. When the temperature of the liquid is raised to $42^{\circ} \mathrm{C}$ the metal piece has a weight of 40 g . If the density of the liquid at $42^{\circ} \mathrm{C}$ is $1.0 \times 10^3 \mathrm{~kg} / \mathrm{m}^3$, then the coefficient of linear expansion of the metal is