An ideal gas is expanded adiabatically at an initial temperature of $300 \ K$ so that its volume is doubled. The final temperature of the hydrogen gas is $(\gamma = 1.40)$.

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

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:

One mole of an ideal gas expands adiabatically at constant pressure such that its temperature $T \propto \frac{1}{\sqrt{V}}$. The value of $\gamma$ for the gas is $(\gamma = \frac{C_p}{C_v}, V = \text{Volume of the gas})$

If a gas of volume $400 \ cc$ at an initial pressure $P$ is suddenly compressed to $100 \ cc$,then its final pressure is (The ratio of the specific heat capacities of the gas at constant pressure and constant volume is $1.5$).

This question has Statement $1$ and Statement $2.$ Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement $1:$ In an adiabatic process,the change in internal energy of a gas is equal to the work done on/by the gas in the process.
Statement $2:$ The temperature of a gas remains constant in an adiabatic process.