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.

$A$ gas at $N.T.P.$ is suddenly compressed to $\left(\frac{1}{4}\right)$ of its original volume. What will be the final pressure? (Given: $\gamma = \text{ratio of specific heats} = \frac{3}{2}$,$P = \text{original pressure}$)

$5.6 \text{ liter}$ of helium gas at $STP$ is adiabatically compressed to $0.7 \text{ liter}$. Taking the initial temperature to be $T_1$,the work done in the process is

For an adiabatic compression of $1 \text{ kmol}$ of gas,$146 \text{ kJ}$ of work is done. During this process,the temperature of the gas increases by $7 \text{ °C}$. The gas is ........

$A$ monoatomic ideal gas is compressed adiabatically to $\left(\frac{1}{27}\right)$ of its initial volume. If the initial temperature of the gas is $T \ K$ and the final temperature is $xT \ K$, the value of $x$ is:

The initial pressure and volume of a given mass of an ideal gas (with $\frac{C_{p}}{C_{V}}=\gamma$), taken in a cylinder fitted with a piston, are $p_{0}$ and $V_{0}$ respectively. At this stage, the gas has the same temperature as that of the surrounding medium, which is $T_{0}$. It is adiabatically compressed to a volume equal to $\frac{V_{0}}{2}$. Subsequently, the gas is allowed to come to thermal equilibrium with the surroundings. What is the heat released to the surrounding?