$A$ 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 efficiency of a Carnot engine,working between the steam point and the ice point,will be $....\,\%$ (in $.81$)

$A$ Carnot engine takes $6000 \,cal$ of heat from a reservoir at $627^{\circ} C$ and gives it to a sink at $27^{\circ} C$. The work done by the engine is ......... $kcal$.

$A$ Carnot engine $(E)$ is working between two temperatures $473 \ K$ and $273 \ K$. In a new system,two engines are used: engine $E_1$ works between $473 \ K$ and $373 \ K$,and engine $E_2$ works between $373 \ K$ and $273 \ K$. If $\eta_{12}$,$\eta_1$,and $\eta_2$ are the efficiencies of the engines $E$,$E_1$,and $E_2$ respectively,then:

$A$ Carnot engine operating between two reservoirs has an efficiency of $\frac{1}{3}$. When the temperature of the cold reservoir is raised by $x$,its efficiency decreases to $\frac{1}{6}$. The value of $x$,if the temperature of the hot reservoir is $99^{\circ} C$,will be $........ K$.

$A$ 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?