$A$ thermodynamic cycle takes in heat energy at a high temperature and rejects energy at a lower temperature. If the amount of energy rejected at the low temperature is $3$ times the amount of work done by the cycle,the efficiency of the cycle is

Three moles of an ideal gas $\left( {{C_P} = \frac{7}{2}R} \right)$ at pressure ${P_A}$ and temperature ${T_A}$ is isothermally expanded to twice its initial volume. It is then compressed at constant pressure to its original volume. Finally, the gas is compressed at constant volume to its original pressure ${P_A}.$ The correct $P-V$ and $P-T$ diagrams indicating the process are

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.

Which of the following is an equivalent cyclic process corresponding to the thermodynamic cycle given in the figure? Where, $1 \rightarrow 2$ is adiabatic.

Two cylinders $A$ and $B$ fitted with pistons contain an equal amount of an ideal rigid diatomic gas at $303 \ K$. The piston of cylinder $A$ is free to move,and that of cylinder $B$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in cylinder $B$ is $49 \ K$,then the rise in temperature of the gas in $A$ is: (in $K$)

The $VT$ curve for a thermodynamic process is given. Identify the corresponding $PV$ curve.