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

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

$A$ gas undergoes a change in which its pressure $P$ and volume $V$ are related as $PV^{n} = \text{constant}$, where $n$ is a constant. If the specific heat of the gas in this change is zero, then the value of $n$ is $(\gamma = \text{adiabatic ratio})$.

$A$ monoatomic gas having $\gamma = 5/3$ is stored in a thermally insulated container and the gas is suddenly compressed to $(1/8)^{th}$ of its initial volume. The ratio of final pressure to initial pressure is: ($\gamma$ is the ratio of specific heats of the gas at constant pressure and at constant volume).

$A$ gas having a volume of $1 \ mm^3$ at $1 \ atm$ pressure is compressed from a temperature of $27^{\circ}C$ to $627^{\circ}C$. What will be the final pressure if the process is adiabatic? (For the gas,$\gamma = 1.5$)

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: