Which of the following is true in the case of an adiabatic process,where $\gamma = C_p / C_V$?

The pressure and density of a diatomic gas $\left(\gamma=\frac{7}{5}\right)$ change adiabatically from $(P, \rho)$ to $(P^{\prime}, \rho^{\prime})$. If $\frac{\rho^{\prime}}{\rho}=32$,then $\frac{P^{\prime}}{P}$ is:

$A$ diatomic gas of volume $2 \ m^3$ at pressure $2 \times 10^5 \ N \ m^{-2}$ is compressed adiabatically to a volume $0.5 \ m^3$. The work done in this process is,$[$Use $4^{1.4} = 6.96]$

Which of the following is the best container for a gas during an adiabatic process?

During an adiabatic process,if the pressure of a gas is found to be proportional to the cube of its absolute temperature,then the ratio of $\frac{C_p}{C_V}$ 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?