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 ..... $^{\circ}C$.

An ideal heat engine operates on a Carnot cycle between $227\,^{\circ}C$ and $127\,^{\circ}C$. It absorbs $6 \times 10^4\, \text{cal}$ at the higher temperature. The amount of heat converted into work is equal to:

$A$ 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:

Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperatures $T_{1}$ and $T_{2}$. The temperature of the hot reservoir of the first engine is $T_{1}$ and the temperature of the cold reservoir of the second engine is $T_{2}$. $T$ is the temperature of the sink of the first engine,which is also the source for the second engine. How is $T$ related to $T_{1}$ and $T_{2}$,if both engines perform equal amounts of work?

$A$ Carnot engine takes $6000 \,cal$ of heat from a reservoir at $627^{\circ} C$ and gives it to a sink at $27^{\circ} C$. The work done by the engine is ......... $kcal$.

When the temperature difference between the source and sink increases,the efficiency of the heat engine