The efficiency of a Carnot engine is $50 \%$ when the temperature of the sink is $500 \ K$. If the efficiency of the Carnot engine is to be increased to $60 \%$,what should be the temperature of the sink,keeping the temperature of the source constant (in $K$)?

Two Carnot engines $A$ and $B$ operate in series such that engine $A$ absorbs heat $Q_1$ at temperature $T_1$ and rejects heat $Q$ to a sink at temperature $T$. Engine $B$ absorbs half of the heat rejected by engine $A$ (i.e.,$Q/2$) and rejects heat $Q_3$ to the sink at temperature $T_3$. When the work done in both cases is equal,the value of $T$ is:

$A$ Carnot engine operates with a source at $227^{\circ}C$ and a sink at $27^{\circ}C$. If the source supplies $50 \ kJ$ of heat energy,the work done by the engine is (in $kJ$)

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 $40 \%$,takes heat from a source maintained at a temperature of $600 \ K$. If it is desired to have an efficiency of $60 \%$,then the intake temperature for the same exhaust (sink) temperature should be: (in $K$)

For an ideal heat engine,the temperature of the source is $127\,^{\circ} C$. In order to have $60\, \%$ efficiency,the temperature of the sink should be $........\,{ }^{\circ} C$. (Round off to the nearest integer)