Work done by a Carnot engine operating between temperatures $127^{\circ}C$ and $27^{\circ}C$ is $2\,kJ$. The amount of heat transferred to the engine by the source is $........\,kJ$.

$A$ reversible engine converts $1/6$ of its input heat into work. When the temperature of the sink is reduced by $62^{\circ}C$,the efficiency of the engine is doubled. Find the temperatures of the source and the sink.

$A$ 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 with its cold body at $17\,^{\circ}C$ has $50\%$ efficiency. If the temperature of its hot body is now increased by $145\,^{\circ}C$,the efficiency becomes...... $\%$

$A$ heat engine receives $200 \, cal$ of heat and rejects $150 \, cal$ of heat. If the temperature of the source is $400 \, K$,what is the temperature of the sink in $K$ (in $, K$)?

$A$ Carnot engine operating between temperatures $T_1$ and $T_2$ has efficiency $\frac{1}{6}$. When $T_2$ is lowered by $60\,K$,its efficiency increases to $\frac{1}{3}$. Then $T_1$ and $T_2$ are respectively: