$A$ 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 $J$):

Explain heat engines and their working.

$A$ Carnot engine has an efficiency of $50 \%$. If the temperature of the sink is reduced by $40 \, K$,its efficiency increases by $30 \%$. The temperature of the source will be $.... \, K$.

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

An ideal heat engine exhausts heat at $77\,^{\circ}C$. To have a $30\%$ efficiency,it must take heat at what temperature in $^{\circ}C$?

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 ............ $m^{3}$.