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:

An ideal heat engine exhausts heat at $77\,^{\circ}C$. To have a $30\%$ efficiency,it must take heat at what temperature in $^{\circ}C$?

What is the efficiency of a heat engine? Write its formula.

$A$ Carnot's heat engine works between the temperatures $427^{\circ} C$ and $27^{\circ} C$. How much heat in $kcal/s$ should it consume per second to deliver mechanical work at the rate of $1.0\,kW$?

Three Carnot engines operate in series between a heat source at temperature $T_1$ and a heat sink at a temperature $T_4$. There are two other reservoirs at temperatures $T_2$ and $T_3$. If the three engines are equally efficient,find the values of $T_2$ and $T_3$ in terms of $T_1$ and $T_4$,given that $T_1 > T_2 > T_3 > T_4$.

$Assertion :$ The Carnot cycle is useful in understanding the performance of heat engines.
$Reason :$ The Carnot cycle provides a way of determining the maximum possible efficiency achievable with reservoirs of given temperatures.