For adiabatic processes $\left( \gamma = \frac{C_p}{C_v} \right)$,which of the following relations is correct?

Can the temperature of an isolated system of gas be changed?

During an adiabatic process,the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of $\frac{C_p}{C_v}$ for the gas is:

An ideal gas at $27^{\circ} C$ is compressed adiabatically to $8/27$ of its original volume. If the ratio of specific heats is $\gamma = 5/3$,then the rise in temperature of the gas is: (in $K$)

Initially,the pressure of $1 \text{ mole}$ of an ideal gas is $10^5 \text{ Nm}^{-2}$ and its volume is $16 \text{ litres}$. When it is adiabatically compressed,its final volume is $2 \text{ litres}$. Calculate the work done on the gas. [Given: Molar specific heat at constant volume $C_v = \frac{3R}{2}$] (in $\text{ kJ}$)

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: