$A$ monoatomic gas is suddenly compressed to $(1/8)^{\text{th}}$ of its initial volume adiabatically. The ratio of the final pressure to initial pressure of the gas is $(\gamma = 5/3)$.

$A$ gas expands adiabatically at constant pressure such that its temperature $T \propto \frac{1}{\sqrt{V}}$. The value of $C_P/C_V$ for the gas is:

$A$ sample of an ideal gas is contained in a cylinder. The volume of the gas is suddenly decreased. $A$ student makes the following statements to explain the change in pressure of the gas:
$I.$ The average kinetic energy of the gas atoms increases.
$II.$ The atoms of the gas hit the walls of the cylinder more frequently.
$III.$ Temperature of the gas remains unchanged.
Which of these statements is true?

Which of the following statements is true? ($\Delta U = \text{increase in internal energy}$,$dW = \text{work done by the system}$)

$A$ diatomic gas $\left(\gamma = \frac{7}{5}\right)$ is compressed adiabatically to volume $\frac{V_0}{32}$,where $V_0$ is its initial volume. The initial temperature of the gas is $T_i$ in Kelvin and the final temperature is $xT_i$ in Kelvin. The value of $x$ is:

$A$ mass of diatomic gas $(\gamma = 1.4)$ at a pressure of $2 \text{ atm}$ is compressed adiabatically so that its temperature rises from $27^{\circ}C$ to $927^{\circ}C$. The pressure of the gas in the final state is ...... $\text{atm}$.