An ideal Carnot engine whose efficiency is $50 \%$ receives heat at $500 \ K$. If the efficiency is to be $60 \%$, then the intake temperature for the same exhaust temperature is: (in $K$)

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

$A$ Carnot engine absorbs $1000\,J$ of heat energy from a reservoir at $127\,^oC$ and rejects $600\,J$ of heat energy during each cycle. The efficiency of the engine and the temperature of the sink will be:

Does a Carnot engine working under an isothermal state perform any useful work?

Consider the given series combination of Carnot cycles. If $W_1 = W_2$,then the value of $T$ is ...... $K$ (all temperatures are maintained at their respective values).

$A$ heat engine operates between a cold reservoir at temperature $T_{2} = 400 \, K$ and a hot reservoir at temperature $T_{1}$. It takes $300 \, J$ of heat from the hot reservoir and delivers $240 \, J$ of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be $.... K$.