The efficiency of a Carnot engine which operates between the two temperatures $T_{1} = 500 \ K$ and $T_{2} = 300 \ K$ is: (in $\%$)

$A$ Carnot engine having efficiency $60 \%$ receives heat from a source at a temperature $600 \text{ K}$. For the same sink temperature, to increase its efficiency to $80 \%$, the temperature of the source is (in $\text{ K}$)

The efficiency of a reversible engine is . . . . . . the efficiency of an irreversible engine.

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.

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

$A$ reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by $62^\circ C$,the efficiency of the engine is doubled. The temperatures of the source and sink are: