For which of the following options will the efficiency of a Carnot engine be the highest?

In a Carnot engine,the temperature of the reservoir is $527^{\circ} C$ and that of the sink is $200 \; K$. If the work done by the engine when it transfers heat from the reservoir to the sink is $12000 \; kJ$,the quantity of heat absorbed by the engine from the reservoir is $x \times 10^{6} \; J$. Find the value of $x$.

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).

Two Carnot engines $A$ and $B$ are operated in series. The first one,$A,$ receives heat at $T_1 = 600 \, K$ and rejects heat to a reservoir at temperature $T_2.$ The second engine $B$ receives the heat rejected by the first engine and,in turn,rejects heat to a reservoir at $T_3 = 400 \, K.$ Calculate the temperature $T_2$ if the work outputs of the two engines are equal. (in $K$)

$A$ Carnot engine operates between $300 \ K$ and $600 \ K$. If the work done per cycle is $800 \ J$,then the heat supplied per cycle is ....... $J/cycle$.

$A$ Carnot engine having efficiency $\frac{1}{6}$ operates between the source temperature $T_H$ and the sink temperature $T_C$. Its efficiency increases to $\frac{1}{3}$ when $T_C$ is decreased by $64 \text{ K}$. The temperatures $T_H$ and $T_C$ are respectively: