Which statement is incorrect?

$A$ reversible heat engine converts one-fourth of the heat input into work. When the temperature of the sink is reduced by $52 \, K$,its efficiency is doubled. The temperature in Kelvin of the source will be ...... .

Consider the given series combination of Carnot cycles. If $W_1 = W_2$,then the value of $T$ is ...... $K$ (all temperatures are maintained at their respective values).

In a Carnot engine,when the temperatures are $T_2 = 0^{\circ} C$ and $T_1 = 200^{\circ} C$,its efficiency is $\eta_1$. When the temperatures are $T_1 = 0^{\circ} C$ and $T_2 = -200^{\circ} C$,its efficiency is $\eta_2$. Then the value of $\frac{\eta_1}{\eta_2}$ is:

Consider a Carnot cycle operating between $T_1 = 500\, K$ and $T_2 = 300\, K$ producing $1\, kJ$ of mechanical work per cycle. Find the heat transferred to the engine by the reservoirs.

In a Carnot engine,as the gas gives heat energy to the sink,the temperature of the sink