The temperature-entropy $(T-S)$ diagram of a reversible engine cycle is given in the figure. Its efficiency is

One mole of an ideal diatomic gas expands from volume $V$ to $2V$ isothermally at a temperature $27^{\circ} C$ and does $W$ joule of work. If the gas undergoes the same magnitude of expansion adiabatically from $27^{\circ} C$ doing the same amount of work $W$, then its final temperature will be (close to) . . . . . . ${ }^{\circ} C$.

$n$ moles of a perfect gas undergo a cyclic process $ABCA$ (see figure) consisting of the following processes:
$A \rightarrow B :$ Isothermal expansion at temperature $T$ so that the volume is doubled from $V_{1}$ to $V_{2}=2V_{1}$ and pressure changes from $P_{1}$ to $P_{2}$.
$B \rightarrow C :$ Isobaric compression at pressure $P_{2}$ to initial volume $V_{1}$.
$C \rightarrow A :$ Isochoric change leading to a change of pressure from $P_{2}$ to $P_{1}$.
Total work done in the complete cycle $ABCA$ is

The ratio of the work done, change in internal energy, and heat absorbed when a diatomic gas expands at constant pressure is

Choose the incorrect statement from the following:
$S1$: The efficiency of a heat engine can be $1$,but the coefficient of performance of a refrigerator can never be infinity.
$S2$: The first law of thermodynamics is basically the principle of conservation of energy.
$S3$: The second law of thermodynamics does not allow several phenomena consistent with the first law.
$S4$: $A$ process,whose sole result is the transfer of heat from a colder to a hotter object,is impossible.

An ideal gas exists in a state with pressure $P_0$, volume $V_0$. It is isothermally expanded to $4$ times its initial volume $(V_0)$, then isobarically compressed to its original volume. Finally, the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is