A) \[{{99}^{o}}C,{{37}^{o}}C\]
B) \[{{124}^{o}}C,{{62}^{o}}C\]
C) \[{{37}^{o}}C,{{99}^{o}}C\]
D) \[{{62}^{o}}C,{{124}^{o}}C\]
Correct Answer: A
Solution :
From \[\eta =1-\frac{{{T}_{2}}}{{{T}_{1}}},\]\[\frac{{{T}_{2}}}{{{T}_{1}}}=1-\eta =1-\frac{1}{6}=\frac{5}{6}\] ?(i) In 2nd case: \[\frac{{{T}_{2}}-62}{{{T}_{1}}}=1-\eta '=1-\frac{2}{6}=\frac{2}{3}\] ?(ii) Using (i), \[{{T}_{2}}-62=\frac{2}{3}{{T}_{1}}=\frac{2}{3}\times \frac{6}{5}{{T}_{2}}=\frac{4}{5}{{T}_{2}}\] or \[\frac{1}{5}{{T}_{2}}=62,\,{{T}_{2}}=310K=310K=310-273={{37}^{o}}C\] \[{{T}_{1}}=\frac{6}{5}{{T}_{2}}=\frac{6}{5}\times 310=372K=372-273={{99}^{o}}C\]
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