$(A)$ Internal energies at $\mathrm{A}$ and $\mathrm{B}$ are the same

$(B)$ Work done by the gas in process $\mathrm{AB}$ is $\mathrm{P}_0 \mathrm{~V}_0 \ln 4$

$(C)$ Pressure at $C$ is $\frac{P_0}{4}$

$(D)$ Temperature at $\mathrm{C}$ is $\frac{\mathrm{T}_0}{4}$

Statement $-I$ : What $\mu$ amount of an ideal gas undergoes adiabatic change from state $\left( P _{1}, V _{1}, T _{1}\right)$ to state $\left( P _{2}, V _{2}, T _{2}\right)$, the work done is $W =\frac{1 R \left( T _{2}- T _{1}\right)}{1-\gamma}$, where $\gamma=\frac{ C _{ P }}{ C _{ V }}$ and $R =$ 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

$A.$ Internal energy of the gas will decrease.

$B.$ Internal energy of the gas will increase.

$C.$ Internal energy of the gas will not change.

$D.$ The gas will do positive work.

$E.$ The gas will do negative work.

Choose the correct answer from the options given below :