$A$ monatomic gas at $630 \,K$ expands adiabatically to $27$ times its initial volume. The final temperature of the gas is (in $\,K$)

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 ....... $J$ $(R = 8.3 \, J/mol \cdot K)$.

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

For an adiabatic expansion of a perfect gas,the value of $\frac{\Delta P}{P}$ is equal to

Consider a cycle tyre being filled with air by a pump. Let $V$ be the volume of the tyre (fixed) and at each stroke of the pump $\Delta V$ ( < < V) of air is transferred to the tube adiabatically. What is the work done when the pressure in the tube is increased from $P_1$ to $P_2$?

An ideal gas at $127^{\circ} C$ is compressed suddenly to $\frac{8}{27}$ of its initial volume. If $\gamma=\frac{5}{3}$ for the ideal gas, then the rise in its temperature is: (in $K$)