When the temperature difference between the source and sink increases,the efficiency of the heat engine

An engine performs $2000 \,J$ of mechanical work and discards $4000 \,J$ of heat each cycle. What is the thermal efficiency of the engine (in $\%$)?

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 $x$.

Determine the efficiency of a Carnot cycle if,in the adiabatic expansion,the volume becomes $3$ times its initial value and $\gamma = 1.5$.

$A$ 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 $kJ$)

In a Carnot engine,the absolute temperature of the source is $25 \%$ more than the absolute temperature of the sink. The efficiency of the engine is (in $\%$)