Two Carnot engines $\mathrm{A}$ and $\mathrm{B}$ are operated in series. Engine A receives heat from a…
Two Carnot engines $\mathrm{A}$ and $\mathrm{B}$ are operated in series. Engine A receives heat from a reservoir at $600 \mathrm{~K}$ and rejects heat to a reservoir at temperature T. Engine B receives heat rejected by engine A and in turn rejects it to a reservoir at $100 \mathrm{~K}$. If the efficiencies of the two engines $\mathrm{A}$ and $\mathrm{B}$ are represented by $\eta_A$ and $\eta_B$ respectively, then what is the value of $\frac{\eta_{\mathrm{A}}}{\eta_{\mathrm{B}}}$
$\frac{12}{7}$
$\frac{12}{5}$
$\frac{5}{12}$
$\frac{7}{12}$
Solution
Efficiency of engine $A, n_A=\frac{T_1-T_2}{T_1}$ and $n_B=\frac{T_2-T_3}{T_2} ; T_2=\frac{T_1+T_3}{2}=350 \mathrm{~K}$ or $\frac{n_A}{n_B}=\frac{\frac{600-350}{600}}{\frac{350-100}{350}}=\frac{7}{12}$