A) \[{{270}^{o}}C\]
B) \[{{1000}^{o}}C\]
C) \[{{727}^{o}}C\]
D) \[{{90}^{o}}C\]
Correct Answer: C
Solution :
: Efficiency of the Carnot engine, \[\eta =1-\frac{{{T}_{2}}}{{{T}_{1}}}\] where \[{{T}_{1}}\] and \[{{T}_{2}}\] are the temperatures of source and sink respectively. Here, \[\eta =70%=\frac{70}{100}=0.7\] \[{{T}_{1}}={{27}^{o}}C=(27+273)K=300K\] \[\therefore \] \[0.7=1-\frac{300}{{{T}_{1}}}\] \[\frac{300}{{{T}_{1}}}=1-0.7=0.3\] \[{{T}_{1}}=\frac{300}{0.3}K=1000K={{(1000-273)}^{o}}C\] \[={{727}^{o}}C\]
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