$A$ Carnot engine works between $27^{\circ} C$ and $127^{\circ} C$. Heat supplied by the source is $500 \ J$. The heat ejected to the sink is (in $J$):

The first operation involved in a Carnot cycle is

$A$ 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 ......... $kcal$.

In a Carnot engine,if the work done during isothermal expansion is $25 \%$ more than the work done during isothermal compression,then the efficiency of the engine is: (in $\%$)

The efficiency of a Carnot engine depends on what,and of what is it independent?

Let $\eta_{1}$ be the efficiency of a Carnot engine at $T_{H}=447^{\circ}C$ and $T_{L}=147^{\circ}C$,while $\eta_{2}$ is the efficiency at $T_{H}=947^{\circ}C$ and $T_{L}=47^{\circ}C$. The ratio $\frac{\eta_{1}}{\eta_{2}}$ will be: