$A$ polyatomic gas $\left( \gamma = \frac{4}{3} \right)$ is compressed to $\frac{1}{8}$ of its volume adiabatically. If its initial pressure is $P_0$,its new pressure will be (in $P_0$)

The relation between volume $(V)$ and absolute temperature $(T)$ of a gas in an adiabatic process is

Two moles of an ideal monoatomic gas occupy a volume $V$ at $27^{\circ}C$. The gas expands adiabatically to a volume $2V$. Calculate $(a)$ the final temperature of the gas and $(b)$ the change in its internal energy.

An ideal gas has a specific heat capacity at constant pressure of $\frac{11}{10} R$. If one mole of this ideal gas at $125^{\circ} C$ does $83 \,J$ of work adiabatically, then the final temperature of the gas would be (Universal gas constant, $R=8.3 \,J \,K^{-1} \,mol^{-1}$ ). (in $^{\circ} C$)

$5$ moles of Hydrogen $\left(\gamma=\frac{7}{5}\right)$ initially at $S.T.P.$ are compressed adiabatically so that its temperature becomes $400^{\circ} C$. The increase in the internal energy of the gas in kilo-joules is $\left(R=8.30 \ J \ mol^{-1} \ K^{-1}\right)$.

$A$ monatomic gas at a pressure of $100 \text{ kPa}$ expands adiabatically such that its final volume becomes $8$ times its initial volume. If the work done during the process is $180 \text{ J}$, then the initial volume of the gas is (in $\text{ cm}^3$)