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

$10 \text{ mole}$ of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from $P_1$ to $P_2$ at constant volume $V = 1 \text{ m}^3$ is $\alpha \text{ Joule}$ ($P_1 = 21.7 \text{ Pa}$,$P_2 = 30 \text{ Pa}$,$C_v = 21 \text{ J/K} \cdot \text{mol}$,$R = 8.3 \text{ J/mol} \cdot \text{K}$). The value of $\alpha$ is . . . . . . .

The work done by a gas is maximum when it expands from a volume $V_1$ to $V_2$. This expansion 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 pressure $P$ of an ideal diatomic gas varies with its absolute temperature $T$ as shown in the figure. The molar heat capacity of the gas during this process is ........... $R$ [$R$ is the gas constant].

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: