Two moles of a gas at a temperature of $327^{\circ} C$ expands adiabatically such that its volume increases by $700 \%$. If the ratio of the specific heat capacities of the gas is $\frac{4}{3}$, then the work done by the gas is (Universal gas constant $= 8.3 \ J \ mol^{-1} \ K^{-1}$) (in $kJ$)

One mole of an ideal gas with $\gamma = 1.4$ is adiabatically compressed so that its temperature rises from $27^{\circ}C$ to $35^{\circ}C$. The change in the internal energy of the gas is ....... $J$ $(R = 8.3 \, J/mol \cdot K)$.

$A$ polyatomic gas is compressed to $\left(\frac{1}{8}\right)^{\text{th}}$ of its original volume adiabatically. If its initial pressure is $P_0$,what will be its new pressure (in $P_0$)? (Given: $\gamma = \frac{C_p}{C_v} = \frac{4}{3}$)

During an adiabatic process, the pressure of a gas is proportional to the cube of its temperature. The value of $C_p / C_V$ for that gas is

$A$ cylindrical vessel of uniform cross-section containing a gas with $\gamma = 1.5$ is divided into two parts $A$ and $B$ using a piston. Initially, the piston is kept fixed such that part $A$ has pressure $p$ and volume $5V$, and part $B$ has pressure $8p$ and volume $V$. If the piston is released and the gas is allowed to undergo an adiabatic process, then the final volume of the gas in part $A$ is:

$A$ diatomic gas initially at $18^oC$ is compressed adiabatically to one-eighth of its original volume. The temperature after compression will be