Question

Two Carnot engines $A$ and $B$ are operated in series. Engine $A$ receives heat from a reservoir at $600K$ and rejects heat to a reservoir heat to reservoir at temperature $T$. Engine $B$ receives heat rejected by engine $A$ and in turn rejects it to a reservoir at $100K$. If the efficiencies of the two engines $A$ and $B$ are represented by ${\eta }_A$ and ${\eta }_B$ respectively, then what is the value of $\frac{{\eta }_B}{{\eta }_A}$

• A. $\frac{12}{7}$
• B. $\frac{12}{5}$
• C. $\frac{5}{12}$
• D. $\frac{7}{12}$

Answer 1

The correct option is A $\frac{12}{7}$

Efficiency is given by ${\eta }_A=1-\frac{T}{600}$ (for engine A)

Efficiency is given by ${\eta }_B=1-\frac{100}{T}$ (for engine B)

The work produced by engine A and B is same so

intermediate temperature $T=\frac{T_1+T_3}{2}$

So T = 350 K

On putting value in efficiency we get 12/7 as answer

So option A is correct