$A$ 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 $\,K$)

Suppose that two heat engines are connected in series,such that the heat released by the first engine is used as the heat absorbed by the second engine,as shown in the figure. The efficiencies of the engines are $\epsilon_1$ and $\epsilon_2$,respectively. The net efficiency of the combination is given by:

Under which ideal condition does the efficiency of a Carnot engine become $100 \%$?

$A$ 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 $K$)

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:

$A$ Carnot heat engine absorbs $600 \ J$ of heat from a source at a temperature of $127^{\circ} C$ and rejects $400 \ J$ of heat to a sink in each cycle. The temperature of the sink is (in $K$)