$A$ sample of $1$ mole of gas at temperature $T$ is adiabatically expanded to double its volume. If the adiabatic constant for the gas is $\gamma = \frac{3}{2}$,then the work done by the gas in the process is:

In the provided figure,there is a cyclic process $ABCDA$ on a sample of $1 \, mol$ of a diatomic gas. The temperatures of the gas during the processes $A \rightarrow B$ and $C \rightarrow D$ are $T_{1}$ and $T_{2}$ $(T_{1} > T_{2})$ respectively. Choose the correct option for the work done if processes $BC$ and $DA$ are adiabatic.

An ideal gas undergoes a process $A \rightarrow B \rightarrow C \rightarrow A$ cycle. The process $A \rightarrow B$ is adiabatic. Calculate the work done in the process $A \rightarrow B$.

In a thermodynamic process, helium gas obeys the law $TP^{-2/5} = \text{constant}$. The heat given to the gas when the temperature of $2$ moles of the gas is raised from $T$ to $4T$ ($R$ is the universal gas constant) is:

Can a change in the internal energy of an ideal gas be considered an adiabatic process?

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