$A$ Carnot heat engine has an efficiency of $50 \%$. The temperature of the sink is maintained at $500 \ K$. To increase the efficiency up to $80 \%$, the required increment in the source temperature is: (in $K$)

$A$ 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 $K$?

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

In a Carnot engine,when the temperatures are $T_2 = 0^{\circ} C$ and $T_1 = 200^{\circ} C$,its efficiency is $\eta_1$. When the temperatures are $T_1 = 0^{\circ} C$ and $T_2 = -200^{\circ} C$,its efficiency is $\eta_2$. Then the value of $\frac{\eta_1}{\eta_2}$ is:

Determine the efficiency of a Carnot cycle if,in the adiabatic expansion,the volume becomes $3$ times its initial value and $\gamma = 1.5$.

If a Carnot engine functions at a source temperature of $127^{\circ}C$ and a sink temperature of $87^{\circ}C$,what is its efficiency in $\%$?