An ideal gas at a pressure of $1 \text{ atm}$ and temperature of $27^{\circ}C$ is compressed adiabatically until its pressure becomes $8$ times the initial pressure. The final temperature is ..... $^{\circ}C$ (given $\gamma = 3/2$).

The temperature of a hypothetical gas increases to $\sqrt{2}$ times when compressed adiabatically to half the volume. Its equation can be written as

$A$ gas at $37^{\circ} C$ is compressed adiabatically to half of its volume. What is the final temperature of the gas (in $^{\circ} C$)? (Ratio of specific heat capacities of the gas is $1.5$)

In a thermodynamic system,$W$ represents the work done by the system and $\Delta U$ is the increase in internal energy. Which of the following statements is $TRUE$?

$A$ monoatomic gas $(\gamma = 5/3)$ initially at $27^{\circ} C$ having volume $V$ is suddenly compressed to one-eighth of its original volume $(V/8)$. What is the final temperature after the compression (in $K$)?

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: