The temperature of the source of a Carnot engine operating with an efficiency of $70\%$ is $1000 \ K$. The temperature of its sink is ...... $K$.

$A$ 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:

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 $x$.

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

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 $6000 \,cal$ 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 ......... $kcal$.