What is the source temperature of the Carnot engine required to get $70 \%$ efficiency (in $^{\circ}C$)? Given sink temperature $= 27^{\circ}C$.

One mole of an ideal monoatomic gas undergoes the following four reversible processes:
Step $1$: It is first compressed adiabatically from volume $V_{1}$ to $1 \; m^{3}$.
Step $2$: Then expanded isothermally to volume $10 \; m^{3}$.
Step $3$: Then expanded adiabatically to volume $V_{3}$.
Step $4$: Then compressed isothermally to volume $V_{1}$.
If the efficiency of the above cycle is $3/4$, then $V_{1}$ is ............ $m^{3}$.

$A$ Carnot engine takes $5000 \, kcal$ of heat from a reservoir at $727 \, ^{\circ}C$ and gives heat to a sink at $127 \, ^{\circ}C$. The work done by the engine is $.......... \times 10^{6} \, J$.

$A$ frictionless heat engine can be $100 \%$ efficient only if its exhaust temperature is ............

The efficiency of a Carnot engine is $50 \%$ when the temperature of the sink is $500 \ K$. If the efficiency of the Carnot engine is to be increased to $60 \%$,what should be the temperature of the sink,keeping the temperature of the source constant (in $K$)?

The efficiency of a Carnot engine is $50\%$ and the temperature of the sink is $500\,K$. If the temperature of the source is kept constant and its efficiency is to be raised to $60\%$,then the required temperature of the sink will be ........... $K$.