A) \[100\,\text{J}\]
B) \[99\text{J}\]
C) \[90\text{J}\]
D) \[1\text{J}\]
Correct Answer: C
Solution :
As, \[{{Q}_{1}}+W={{Q}_{2}}\] Given, \[\eta =\frac{1}{10}\] Now, using \[\eta =1-\frac{{{T}_{1}}}{{{T}_{2}}}\] So, \[\frac{1}{10}=1-\frac{{{T}_{1}}}{{{T}_{2}}}\] \[\Rightarrow \,\,\,\frac{{{T}_{1}}}{{{T}_{2}}}=\frac{9}{10}\] Now \[\frac{{{Q}_{1}}}{{{Q}_{2}}}=\frac{{{T}_{1}}}{{{T}_{2}}}\] \[\Rightarrow \,\,\,\frac{{{Q}_{1}}}{{{Q}_{1}}+W}=\frac{9}{10}\] \[\Rightarrow \] \[10{{Q}_{1}}\,=9{{Q}_{1}}\,+9W\] \[\Rightarrow \,\,\,\,\,\,{{Q}_{1}}=9W=9\times 10=90J\]
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