An ideal heat engine based on the Carnot cycle operates between temperatures of $227 \, ^\circ C$ and $127 \, ^\circ C$. If it absorbs $6 \times 10^{4} \, cal$ of heat from the high-temperature reservoir,the net work done by the engine is:

An ideal heat engine exhausting heat at $77^{\circ}C$ is to have a $30\%$ efficiency. It must take heat at ...... $^{\circ}C$.

$A$ Carnot engine working between $300 \ K$ and $400 \ K$ produces $800 \ J$ of useful work. The amount of heat energy supplied to the engine from the source is: (in $J$)

$A$ Carnot engine has the same efficiency between $800 \ K$ and $500 \ K$ and between $x \ K$ and $600 \ K$. The value of '$x$' is: (in $K$)

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 $K$)

Explain why the efficiency of a Carnot engine cannot be $100\%$?