Efficiency of a heat engine whose sink is at temperature of $300 \,K$ is $40 \%$. To increase the efficiency to $60 \%$, keeping the sink temperature constant, the source temperature must be increased by (in $\,K$)

$A$ 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 $K$)?$

Consider a Carnot engine working between $T_1 = 500 \ K$ and $T_2 = 300 \ K$ producing $1 \ kJ$ of mechanical work per cycle. Calculate the heat absorbed by the engine from the source. (in $kJ$)

$A$ Carnot engine with efficiency $\eta$ operates between two heat reservoirs with temperatures $T_1$ and $T_2$, where $T_1 > T_2$. If only $T_1$ is changed by $0.4 \%$, the change in efficiency is $\Delta \eta_1$, whereas if only $T_2$ is changed by $0.2 \%$, the efficiency is changed by $\Delta \eta_2$. The ratio $\frac{\Delta \eta_1}{\Delta \eta_2}$ is approximately,

$A$ Carnot engine whose efficiency is $40 \%$, receives heat at $500 \ K$. If the efficiency is to be $50 \%$, the source temperature for the same exhaust temperature is (in $K$)

The efficiency of a Carnot engine operating between reservoirs maintained at temperatures $27^{\circ}C$ and $-123^{\circ}C$ is ...... $\%$