In the reported figure, there is a cyclic process $ABCDA$ on a sample of $1\, {mol}$ of a diatomic gas. The temperature of the gas during the process ${A} \rightarrow {B}$ and ${C} \rightarrow {D}$ are ${T}_{1}$ and ${T}_{2}\left({T}_{1}\,>\,{T}_{2}\right)$ respectively.

Choose the correct option out of the following for work done if processes $B C$ and $D A$ are adiabatic.

The equation of state for a gas is given by $PV = nRT + \alpha V$, where $n$ is the number of moles and $\alpha $ is a positive constant. The initial temperature and pressure of one mole of the gas contained in a cylinder are $T_o$ and $P_o$ respectively. The work done by the gas when its temperature doubles isobarically will be

A balloon filled with helium $\left(32^{\circ} C \right.$ and $1.7\; atm$.) bursts. Immediately afterwards the expansion of helium can be considered as

During an adiabatic expansion of $2\, moles$ of a gas, the change in internal energy was found $-50J.$ The work done during the process is …… $J$

An engine takes in $5$ moles of air at $20\,^{\circ} C$ and $1$ $atm,$ and compresses it adiabaticaly to $1 / 10^{\text {th }}$ of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules, the change in its internal energy during this process comes out to be $X\, kJ$. The value of $X$ to the nearest integer is