An ideal gas having pressure $P$, volume $V$, and temperature $T$ undergoes a thermodynamic process in which $dW = 0$ and $dQ < 0$. Then, for the gas

In a thermodynamic isobaric process:

The ratio of specific heats of a gas is $\gamma$. The change in internal energy of one mole of the gas, when the volume changes from $V$ to $2V$ at constant pressure $p$, is:

The thermodynamic process in which the work done on or by the gas is zero is:

If $\gamma$ is the ratio of molar specific heat at constant pressure to molar specific heat at constant volume for a gas,find the change in internal energy of $1 \, mol$ of the gas when its volume changes from $V$ to $2V$ at constant pressure $P$.

The state of a thermodynamic system changes from $(1)$ $(P_1, V)$ to $(2P_1, V)$ and $(2)$ $(P, V_1)$ to $(P, 2V_1)$. The work done during these two processes is respectively: