Compressed air in the tube of a wheel of a cycle at normal temperature suddenly starts coming out from a puncture. The air inside

In the provided figure,there is a cyclic process $ABCDA$ on a sample of $1 \, mol$ of a diatomic gas. The temperatures of the gas during the processes $A \rightarrow B$ and $C \rightarrow D$ are $T_{1}$ and $T_{2}$ $(T_{1} > T_{2})$ respectively. Choose the correct option for the work done if processes $BC$ and $DA$ are adiabatic.

$A$ monoatomic gas at pressure $P$ and volume $V$ is suddenly compressed to one-eighth of its original volume. The final pressure at constant entropy will be $.....P$.

$A$ diatomic gas $\left(\gamma = \frac{7}{5}\right)$ is compressed adiabatically to volume $\frac{V_0}{32}$,where $V_0$ is its initial volume. The initial temperature of the gas is $T_i$ in Kelvin and the final temperature is $xT_i$ in Kelvin. The value of $x$ is:

$\Delta U + \Delta W = 0$ is valid for

$A$ monatomic gas at $630 \,K$ expands adiabatically to $27$ times its initial volume. The final temperature of the gas is (in $\,K$)