The efficiency of a heat engine that works between the temperatures where Celsius-Fahrenheit scales coincide and Kelvin-Fahrenheit scales coincide is (approximately) (in $\%$)

One mole of an ideal monoatomic gas undergoes the following four reversible processes:
Step $1$: It is first compressed adiabatically from volume $V_{1}$ to $1 \; m^{3}$.
Step $2$: Then expanded isothermally to volume $10 \; m^{3}$.
Step $3$: Then expanded adiabatically to volume $V_{3}$.
Step $4$: Then compressed isothermally to volume $V_{1}$.
If the efficiency of the above cycle is $3/4$, then $V_{1}$ is ............ $m^{3}$.

Temperature of a cold reservoir of a Carnot engine is $127^{\circ} C$. If the efficiency of the Carnot engine is $20 \%$,then the temperature of the hot reservoir is (in $^{\circ} C$)

Three Carnot engines operate in series between a heat source at a temperature $T_1$ and a heat sink at temperature $T_4$ (see figure). There are two other reservoirs at temperatures $T_2$ and $T_3$,as shown,with $T_1 > T_2 > T_3 > T_4$. The three engines are equally efficient if

$A$ Carnot engine whose efficiency is $40 \%$, receives heat at $500 \ K$. If the efficiency is to be $50 \%$, the source temperature for the same exhaust temperature is (in $K$)

Determine the efficiency of a Carnot cycle if,in the adiabatic expansion,the volume becomes $3$ times its initial value and $\gamma = 1.5$.