The temperature of the sink of a Carnot engine is $27^\circ C$. The efficiency of the engine is $25\%$. Then the temperature of the source is ...... $^\circ C$.

$A$ Carnot engine operating between temperatures $T_1$ and $T_2$ has efficiency $\frac{1}{6}$. When $T_2$ is lowered by $60\,K$,its efficiency increases to $\frac{1}{3}$. Then $T_1$ and $T_2$ are respectively:

Three Carnot engines operate in series between a heat source at temperature $T_1$ and a heat sink at a temperature $T_4$. There are two other reservoirs at temperatures $T_2$ and $T_3$. If the three engines are equally efficient,find the values of $T_2$ and $T_3$ in terms of $T_1$ and $T_4$,given that $T_1 > T_2 > T_3 > T_4$.

Efficiency of a heat engine whose sink is at temperature of $300 \,K$ is $40 \%$. To increase the efficiency to $60 \%$, keeping the sink temperature constant, the source temperature must be increased by (in $\,K$)

The efficiency of a Carnot heat engine is $0.5$ when the temperature of the source is $T_{1}$ and that of the sink is $T_{2}$. The efficiency of another Carnot heat engine is also $0.5$. The temperatures of the source and sink of the second engine are respectively:

An engine has an efficiency of $0.25$ when the temperature of the sink is reduced by $58\,^{\circ}C$,its efficiency is doubled. The temperature of the source is ..... $^{\circ}C$.