A Carnot engine (E) is working between two temperatures 473 K and 273 K. In a new system two engines - engine E_1 works between 473 K to 373 K and…

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