In a Carnot engine,the absolute temperature of the source is $25 \%$ more than the absolute temperature of the sink. The efficiency of the engine is (in $\%$)

$A$ Carnot engine absorbs heat from a reservoir maintained at temperature $1000 \,K$. The engine rejects heat to a reservoir whose temperature is $T$. If the magnitude of absorbed heat is $400 \,J$ and work performed is $300 \,J$, then the value of $T$ is (in $\,K$)

Explain why the efficiency of a Carnot engine cannot be $100\%$?

Temperature of a cold reservoir of a Carnot engine is $127^{\circ} C$. If the efficiency of the Carnot engine is $20 \%$,then the temperature of the hot reservoir is (in $^{\circ} C$)

Show the four steps of a Carnot engine in a $P-V$ graph,write the equation for each step,and obtain the work done by the system. Also,derive the efficiency of a Carnot engine.

$A$ Carnot heat engine absorbs $600 \ J$ of heat from a source at a temperature of $127^{\circ} C$ and rejects $400 \ J$ of heat to a sink in each cycle. The temperature of the sink is (in $K$)