For an adiabatic expansion of an ideal gas,the fractional change in its pressure is equal to (where $\gamma$ is the ratio of specific heats):

Given below are two statements:
Statement-$I$: When $\mu$ amount of an ideal gas undergoes adiabatic change from state $(P_1, V_1, T_1)$ to state $(P_2, V_2, T_2)$,the work done is $W = \frac{\mu R(T_2 - T_1)}{1 - \gamma}$,where $\gamma = \frac{C_P}{C_V}$ and $R$ is the universal gas constant.
Statement-$II$: In the above case,when work is done on the gas,the temperature of the gas would rise.
Choose the correct answer from the options given below:

In an adiabatic process,the state of a gas is changed from $(P_1, V_1, T_1)$ to $(P_2, V_2, T_2)$. Which of the following relations is correct?

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.

In a thermodynamic process,there is no exchange of heat between the system and surroundings. Then the thermodynamic process is

The initial pressure and volume of an ideal gas are $P_0$ and $V_0$. The final pressure of the gas when the gas is suddenly compressed to volume $\frac{V_0}{4}$ will be (Given $\gamma =$ ratio of specific heats at constant pressure and at constant volume).