$A$ Carnot heat engine has an efficiency of $50 \%$. The temperature of the sink is maintained at $500 \ K$. To increase the efficiency up to $80 \%$, the required increment in the source temperature is: (in $K$)

$A$ 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 (in $K$)

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.

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

$A$ Carnot engine whose heat sink is at $27^{\circ} C$ has an efficiency of $40 \%$. By how much should its source temperature be changed so as to increase its efficiency to $60 \% (in $K$)?$

$A$ 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 $\,K$)