What is the source temperature of the Carnot engine required to get $70 \%$ efficiency (in $^{\circ}C$)? Given sink temperature $= 27^{\circ}C$.

An ideal Carnot engine,whose efficiency is $40 \%$ receives heat at $500 \; K$. If its efficiency is $50 \%$ then the intake temperature for the same exhaust temperature is ......... $K$.

$A$ Carnot cycle consists of

$A$ scientist claims that the efficiency of their heat engine,which operates between a source temperature of $127^{\circ}C$ and a sink temperature of $27^{\circ}C$,is $26\%$. Then:

$A$ Carnot engine,whose efficiency is $40\%$,takes in heat from a source maintained at a temperature of $500\ K$. It is desired to have an engine of efficiency $60\%$. Then,the intake temperature for the same exhaust (sink) temperature must be ....... $K$.

Two Carnot engines $A$ and $B$ are operated in series. The first one,$A,$ receives heat at $T_1 = 600 \, K$ and rejects heat to a reservoir at temperature $T_2.$ The second engine $B$ receives the heat rejected by the first engine and,in turn,rejects heat to a reservoir at $T_3 = 400 \, K.$ Calculate the temperature $T_2$ if the work outputs of the two engines are equal. (in $K$)