In an adiabatic expansion,which of the following is true?

$A$ 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).

An ideal gas at atmospheric pressure is adiabatically compressed so that its density becomes $32$ times its initial value. If the final pressure of the gas is $128$ atmospheres,the value of $\gamma$ for the gas is:

$A$ monatomic gas at pressure $P_1$ and volume $V_1$ is compressed adiabatically to $1/8$ of its original volume. What is the final pressure of the gas in terms of $P_1$?

$A$ certain mass of gas at $273 \ K$ is expanded to $81$ times its volume under adiabatic condition. If $\gamma = 1.25$ for the gas, then its final temperature is ..... $^\circ C$

The pressure and density of a diatomic gas $(\gamma = 7/5)$ change adiabatically from $(P, d)$ to $(P', d')$. If $\frac{d'}{d} = 32$,then $\frac{P'}{P}$ is equal to: