$A$ Carnot engine $(E)$ is working between two temperatures $473 \ K$ and $273 \ K$. In a new system,two engines are used: engine $E_1$ works between $473 \ K$ and $373 \ K$,and engine $E_2$ works between $373 \ K$ and $273 \ K$. If $\eta_{12}$,$\eta_1$,and $\eta_2$ are the efficiencies of the engines $E$,$E_1$,and $E_2$ respectively,then:

$A$ Carnot's heat engine works between the temperatures $427^{\circ} C$ and $27^{\circ} C$. How much heat in $kcal/s$ should it consume per second to deliver mechanical work at the rate of $1.0\,kW$?

$A$ Carnot engine operates between $227^{\circ}C$ and $27^{\circ}C$. The efficiency of the engine will be:

When the absolute temperature of the source of a Carnot heat engine is increased by $25 \%$,its efficiency increases by $80 \%$. The new efficiency of the engine is (in $\%$)

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: Efficiency of a reversible heat engine will be highest at $-273^{\circ} C$ temperature of cold reservoir.
Reason $R$: The efficiency of Carnot's engine depends not only on the temperature of the cold reservoir but it depends on the temperature of the hot reservoir too and is given as $\eta = (1 - \frac{T_2}{T_1})$.
In the light of the above statements,choose the correct answer from the options given below:

Explain heat engines and their working.