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11.Thermodynamics
normal
Two Carnot engines $A$ and $B$ are operated in series. The engine $A$ receives heat from the source at temperature $T_1$ and rejects the heat to the sink at temperature $T$. The second engine $B$ receives the heat at temperature $T$ and rejects to its sink at temperature $T_2$. For what value of $T$ the efficiencies of the two engines are equal?
A
$\frac{{{T_1} + {T_2}}}{2}$
B
$\frac{{{T_1} - {T_2}}}{2}$
C
${{T_1}{T_2}}$
D
${\sqrt {{T_1}{T_2}} }$
Solution
${{\rm{n}}_1} = 1 – \frac{{\rm{T}}}{{{{\rm{T}}_1}}}\quad $
${{\rm{n}}_2} = 1 – \frac{{{{\rm{T}}_2}}}{{\rm{T}}}\quad $
${{\rm{n}}_1} = {{\rm{n}}_2}\quad \frac{{\rm{T}}}{{{{\rm{T}}_1}}} = \frac{{{{\rm{T}}_2}}}{{\rm{T}}}$
$\mathrm{T}=\sqrt{\mathrm{T}_{1} \mathrm{T}_{2}}$
Standard 11
Physics
