The efficiency of a Carnot heat engine is $25 \%$ and the temperature of its source is $127^{\circ} C$. Without changing the temperature of the source,if the absolute temperature of the sink is decreased by $10 \%$,the new efficiency of the engine is: (in $\%$)

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 .... $J$.

$A$ heat engine operates with the cold reservoir at a temperature of $324 \; K$. If the heat engine takes $300 \; J$ of heat from the hot reservoir and delivers $180 \; J$ of heat to the cold reservoir per cycle,what is the minimum temperature of the hot reservoir in $K$?

The Carnot cycle (reversible) of a gas represented by a Pressure-Volume $(P-V)$ curve is shown in the diagram. Consider the following statements:
$I.$ Area $ABCD =$ Work done by the gas
$II.$ Area $ABCD =$ Net heat absorbed
$III.$ Change in the internal energy in the cycle $= 0$
Which of these are correct?

Consider a two-stage Carnot engine. In the first stage, heat $Q_1$ is absorbed at temperature $T$ and heat $Q_2$ is expelled at temperature $\alpha T$ (where $\alpha < 1$). In the second stage, heat $Q_2$ is absorbed at temperature $\alpha T$ and heat $Q_3$ is expelled at temperature $\beta T$ (where $\beta < \alpha$). The efficiency of the Carnot engine will be

$A$ Carnot engine whose heat sink is at $27\,^{\circ} C$ has an efficiency of $25 \%$. By how many degrees should the temperature of the source be changed to increase the efficiency by $100 \%$ of the original efficiency?