A) \[T=\frac{{{T}_{1}}+{{T}_{2}}}{2}\]
B) \[T=\sqrt{{{T}_{1}}{{T}_{2}}}\]
C) \[T=\frac{2{{T}_{1}}{{T}_{2}}}{{{T}_{1}}+{{T}_{2}}}\]
D) \[T=0\]
Correct Answer: A
Solution :
[a] Let\[{{Q}_{1}}\]: Heat input to first engine |
\[{{Q}_{C}}\]: Heat rejected by first engine |
\[{{Q}_{2}}\]: Heat rejected by second engine |
\[{{T}_{C}}\]: Lower temperature of first engine |
\[W={{Q}_{1}}{{Q}_{C}}={{Q}_{C}}{{Q}_{2}}\] |
\[\Rightarrow \,\,\,\,2{{Q}_{C}}={{Q}_{1}}+{{Q}_{2}}\] |
\[\Rightarrow 2{{T}_{C}}={{T}_{1}}+{{T}_{2}}\Rightarrow {{T}_{C}}={{T}_{1}}+{{T}_{2}}\] |
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