What is the theoretical efficiency of a heat engine?

$A$ 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 engine working between $300\,K$ and $600\,K$ has a work output of $800\,J$ per cycle. What is the amount of heat energy supplied to the engine from the source per cycle in $J/cycle$?

Consider the given series combination of Carnot cycles. If $W_1 = W_2$,then the value of $T$ is ...... $K$ (all temperatures are maintained at their respective values).

$A$ Carnot engine whose efficiency is $40 \%$,receives heat at $500 \ K$. If the efficiency is to be $50 \%$,the source temperature for the same exhaust temperature is (in $K$)

$A$ Carnot engine uses an ideal monoatomic gas first and then an ideal diatomic gas. If the source and sink temperatures are $411^{\circ}C$ and $69^{\circ}C$ respectively,and the engine extracts $1000 \, J$ of heat in each cycle,then the area enclosed by the $PV$ diagram is ........ $J$.