A) \[1.6\times {{10}^{4}}J\]
B) \[1.2\times {{10}^{4}}J\]
C) \[4.8\times {{10}^{4}}J\]
D) \[3.5\times {{10}^{4}}J\]
Correct Answer: B
Solution :
Using the relation \[\frac{W}{{{Q}_{1}}}=\frac{{{Q}_{1}}-{{Q}_{2}}}{{{Q}_{1}}}\] or \[\frac{W}{{{Q}_{1}}}=1-\frac{{{Q}_{2}}}{{{Q}_{1}}}\] or \[\frac{W}{{{Q}_{1}}}=1-\frac{{{T}_{2}}}{{{T}_{1}}}\] \[\left( \because \frac{{{Q}_{1}}}{{{Q}_{2}}}=\frac{{{T}_{1}}}{{{T}_{2}}} \right)\] or \[W={{Q}_{1}}\,\left( 1-\frac{{{T}_{2}}}{{{T}_{1}}} \right)\] \[\therefore \] \[W=6\times {{10}^{-4}}\left[ 1-\frac{(127+273)}{(227+273)} \right]\] or \[W=6\times {{10}^{4}}\left( 1-\frac{400}{500} \right)\] \[=6\times {{10}^{4}}\times \frac{100}{500}\] \[=1.2\times {{10}^{4}}J\]
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