An ideal heat engine operates in a Carnot cycle between $127^{\circ} C$ and $27^{\circ} C$. It absorbs $5 \times 10^4 \text{ cal}$ of heat at the higher temperature. The amount of heat converted to work is:

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 $K$)

$A$ scientist claims that the efficiency of their heat engine,which operates between a source temperature of $127^{\circ}C$ and a sink temperature of $27^{\circ}C$,is $26\%$. Then:

An engine performs $2000 \,J$ of mechanical work and discards $4000 \,J$ of heat each cycle. What is the thermal efficiency of the engine (in $\%$)?

What is the common feature of a heat engine based on a cyclic process?

An engine operating between the boiling and freezing points of water will have:
$1.$ Efficiency more than $27 \%$
$2.$ Efficiency less than the efficiency of a Carnot engine operating between the same two temperatures.
$3.$ Efficiency equal to $27 \%$
$4.$ Efficiency less than $27 \%$