$A$ Carnot engine whose sink is at $300\, K$ has an efficiency of $40\%.$ By how much should the temperature of the source be increased so as to increase its efficiency by $50\%$ of its original efficiency? (in $K$)

$A$ Carnot engine whose heat sink is at $27\,^{\circ} C$ has an efficiency of $25 \%$. By how many degrees should the temperature of the source be changed to increase the efficiency by $100 \%$ of the original efficiency?

The ratio of the efficiencies of two Carnot engines $A$ and $B$ is $1.25$. The temperature difference between the source and the sink is the same in both engines. The ratio of the absolute temperatures of the sources of engines $A$ and $B$ is

$300 \, cal$ of heat is given to a heat engine and it rejects $225 \, cal$ of heat. If the source temperature is $227^{\circ} C$,then the temperature of the sink will be . . . . . . $^{\circ} C$.

$A$ 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 $\,K$)

What is a Carnot cycle? Explain it by drawing a figure.