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 $........\,kJ$.

$A$ 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 $\left( \frac{\eta_2}{\eta_1} \right)$ of the engine in the two cases is:

$A$ Carnot engine takes $300$ calories of heat from a source at $500 \,K$ and rejects $150$ calories of heat to the sink. The temperature of the sink is (in $\,K$)

$A$ Carnot engine has an efficiency of $50\%$ when its source is at a temperature $327^{\circ}C$. The temperature of the sink is $.........^{\circ}C$.

An engine operating between the boiling and freezing points of water will have:
$1.$ Efficiency more than $27 \%$
$2.$ Efficiency less than the efficiency of a Carnot engine operating between the same two temperatures.
$3.$ Efficiency equal to $27 \%$
$4.$ Efficiency less than $27 \%$

$A$ reversible engine and an irreversible engine are working between the same temperatures. The efficiency of the ...........