$A$ 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 $kJ$)

Two Carnot engines $A$ and $B$ are operated in series. Engine $A$ receives heat from a reservoir at $600\,K$ and rejects heat to a reservoir at temperature $T$. Engine $B$ receives heat rejected by engine $A$ and in turn rejects it to a reservoir at $100\,K$. If the efficiencies of the two engines $A$ and $B$ are equal,what is the value of the intermediate temperature $T$ and the ratio of their efficiencies $\frac{\eta_A}{\eta_B}$?

The temperature of the sink of a Carnot engine is $250 \ K$. In order to increase the efficiency of the Carnot engine from $25 \%$ to $50 \%$,the temperature of the sink should be increased by

Let $\eta_{1}$ be the efficiency of a Carnot engine at $T_{H}=447^{\circ}C$ and $T_{L}=147^{\circ}C$,while $\eta_{2}$ is the efficiency at $T_{H}=947^{\circ}C$ and $T_{L}=47^{\circ}C$. The ratio $\frac{\eta_{1}}{\eta_{2}}$ will be:

$A$ Carnot engine working between $300 \ K$ and $400 \ K$ produces $800 \ J$ of useful work. The amount of heat energy supplied to the engine from the source is: (in $J$)

$A$ 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 $K$)