During an adiabatic process,the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of $\frac{C_P}{C_V}$ for the gas is

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

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

$A$ bicycle tire tube is inflated using a pump. Assume the volume of the tube $V$ is constant and in each stroke,an amount of air $\Delta V$ is pushed into the tube under an adiabatic process. What is the work done to increase the pressure in the tube from $P_{1}$ to $P_{2}$?

The work done in which of the following processes is equal to the internal energy of the system?

An ideal monoatomic gas of volume $V$ is adiabatically expanded to a volume $3V$ at $27^{\circ}C$. The final temperature in Kelvins is (use $\frac{C_P}{C_V} = \frac{5}{3}$)