An ideal gas heat engine operates in a Carnot cycle between $227^{\circ}C$ and $127^{\circ}C$. It absorbs $6 \times 10^4 \text{ cal}$ of heat at the higher temperature. The amount of heat converted to work is ......... $\times 10^4 \text{ cal}$.

Suppose that two heat engines are connected in series,such that the heat exhaust of the first engine is used as the heat input of the second engine as shown in the figure. The efficiencies of the engines are $\eta_1$ and $\eta_2$,respectively. The net efficiency of the combination is given by

$A$ heat engine receives $200 \, cal$ of heat and rejects $150 \, cal$ of heat. If the temperature of the source is $400 \, K$,what is the temperature of the sink in $K$ (in $, K$)?

The efficiency of a Carnot engine is $0.6$. It rejects a total of $20 \ J$ of heat. The work done by the engine is .... $J$.

The efficiency of a Carnot engine is $50\%$ and the temperature of the sink is $500\,K$. If the temperature of the source is kept constant and its efficiency is to be raised to $60\%$,then the required temperature of the sink will be ........... $K$.

$A$ Carnot cycle operating between $T_H = 600 \ K$ and $T_C = 300 \ K$ produces $1.5 \ kJ$ of mechanical work per cycle. The heat transferred to the engine by the reservoir is: (in $kJ$)