During an adiabatic process,the pressure of the gas is found to be proportional to the cube of its absolute temperature. The ratio $C_P/C_V = \gamma$ for the gas is:

$A$ gas for which $\gamma = 1.5$ is suddenly compressed to $\frac{1}{4}$ of its initial volume. What is the ratio of the final pressure to the initial pressure?

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 $(\gamma = \frac{C_p}{C_v}, V = \text{Volume of the gas})$

$200 \ cc$ of an ideal gas $(\gamma = 1.5)$ expands adiabatically. If the rms speed of the gas molecules becomes half of the initial value,the final volume of the gas is (in $cc$)

Work done on heating one mole of monoatomic gas adiabatically through $20^{\circ} C$ is $W$. Then,the work done on heating $6$ moles of rigid diatomic gas through the same change in temperature is: (in $W$)

In an adiabatic process,the state of a gas is changed from $(P_1, V_1, T_1)$ to $(P_2, V_2, T_2)$. Which of the following relations is correct?