The efficiency of a Carnot engine is $\eta$ when its hot and cold reservoirs are maintained at temperatures $T_1$ and $T_2$, respectively. To increase the efficiency to $1.5 \eta$, the increase in temperature $(\Delta T)$ of the hot reservoir, while keeping the cold reservoir constant at $T_2$, is

What is a heat engine?

$A$ heat engine operating between temperatures $T_1$ and $T_2$ has an efficiency of $\frac{1}{6}$. When $T_2$ is lowered by $62 \ K$,its efficiency increases to $\frac{1}{3}$. Then $T_1$ and $T_2$ respectively are:

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: Efficiency of a reversible heat engine will be highest at $-273^{\circ} C$ temperature of cold reservoir.
Reason $R$: The efficiency of Carnot's engine depends not only on the temperature of the cold reservoir but it depends on the temperature of the hot reservoir too and is given as $\eta = (1 - \frac{T_2}{T_1})$.
In the light of the above statements,choose the correct answer from the options given below:

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

$A$ Carnot's engine operates with a source at $127^{\circ} C$ and a sink at $27^{\circ} C$. If the source supplies $40 \ kJ$ of heat energy,the work done by the engine is (in $kJ$)