$A$ cyclic process $ABCD$ is shown in the given $P-V$ diagram. The $P-T$ diagram that represents the same process 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.

The relation between efficiency $(\eta)$ of a Carnot engine and the coefficient of performance $(\beta)$ of a refrigerator working between the same temperatures is:

In the thermodynamic processes, which of the following statements is $NOT$ true?

Two moles of a monoatomic ideal gas is confined in a container and is heated such that its temperature increases by $10\,^{\circ}C$. The approximate change in its internal energy is ..... $J$. $(R = 8.31\, J/mol\cdot K)$

Consider two containers $A$ and $B$ containing monoatomic gases at the same Pressure $(P)$,Volume $(V)$ and Temperature $(T)$. The gas in $A$ is compressed isothermally to $\frac{1}{8}$ of its original volume while the gas $B$ is compressed adiabatically to $\frac{1}{8}$ of its original volume. The ratio of final pressure of gas in $B$ to that of gas in $A$ is ...........