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.

Three processes compose a thermodynamic cycle shown in the $PV$ diagram. Process $1\rightarrow 2$ takes place at constant temperature. Process $2\rightarrow 3$ takes place at constant volume,and process $3\rightarrow 1$ is adiabatic. During the complete cycle,the total amount of work done is $10\,J$. During process $2\rightarrow 3$,the internal energy decreases by $20\,J$ and during process $3\rightarrow 1$,$20\,J$ of work is done on the system. How much heat is added to the system during process $1\rightarrow 2$ (in $,J$)?

When an ideal gas is heated at constant pressure,what percentage of the heat supplied is used to perform external work? $(\gamma = 5/3)$

One mole of an ideal monoatomic gas undergoes the following four reversible processes:
Step $1$: It is first compressed adiabatically from volume $8.0 \, m^{3}$ to $1.0 \, m^{3}$.
Step $2$: Then expanded isothermally at temperature $T_{1}$ to volume $10.0 \, m^{3}$.
Step $3$: Then expanded adiabatically to volume $80.0 \, m^{3}$.
Step $4$: Then compressed isothermally at temperature $T_{2}$ to volume $8.0 \, m^{3}$.
Then,$T_{1} / T_{2}$ is:

$A$ cyclic process $ABCD$ is shown in the $p-V$ diagram. Which of the following curves represents the same process if $BC$ and $DA$ are isothermal processes?

Air in a cylinder is suddenly compressed by a piston,which is then maintained at the same position. With the passage of time,