$A$ Carnot engine is made to work between $200^{\circ}C$ and $0^{\circ}C$ first and then between $0^{\circ}C$ and $-200^{\circ}C$. The ratio of efficiencies of the engine in the two cases is

In a Carnot engine,the temperature of the reservoir is $527^{\circ} C$ and that of the sink is $200 \; K$. If the work done by the engine when it transfers heat from the reservoir to the sink is $12000 \; kJ$,the quantity of heat absorbed by the engine from the reservoir is $x \times 10^{6} \; J$. Find the value of $x$.

$A$ Carnot engine has an efficiency of $50 \%$. If the temperature of the sink is reduced by $40 \, K$,its efficiency increases by $30 \%$. The temperature of the source will be $.... \, K$.

The maximum possible efficiency of a heat engine is ...........

Give the basic features of a heat engine based on a cyclic process and obtain the formula for its efficiency.

$A$ Carnot's engine operates with a source at $127^{\circ} C$ and a sink at $27^{\circ} C$. If the source supplies $40 \ kJ$ of heat energy,the work done by the engine is (in $kJ$)