An ideal heat engine working between temperatures $T_1$ and $T_2$ has an efficiency $\eta$. What will be the new efficiency if both the source and sink temperatures are doubled?

$A$ Carnot cycle consists of

$A$ reversible heat engine converts one-fourth of the heat input into work. When the temperature of the sink is reduced by $52 \, K$,its efficiency is doubled. The temperature in Kelvin of the source will be ...... .

Work done by a Carnot engine operating between temperatures $127^{\circ}C$ and $27^{\circ}C$ is $2\,kJ$. The amount of heat transferred to the engine by the source is $........\,kJ$.

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 ............ $m^{3}$.

Suppose that two heat engines are connected in series,such that the heat released by the first engine is used as the heat absorbed by the second engine,as shown in the figure. The efficiencies of the engines are $\epsilon_1$ and $\epsilon_2$,respectively. The net efficiency of the combination is given by: