A) \[4.2\times {{10}^{6}}\,J\]
B) \[8.4\times {{10}^{6}}\,J\]
C) \[16.8\times {{10}^{6}}\,J\]
D) 0
Correct Answer: B
Solution :
\[{{T}_{1}}=627+273=900\,K\] \[{{Q}_{1}}=3\times {{10}^{2}}\,\text{cal}\] \[{{T}_{2}}=27+273=300\,K\] \[\therefore \] \[\frac{{{Q}_{1}}}{{{T}_{1}}}=\frac{{{Q}_{2}}}{{{T}_{2}}}\] \[\Rightarrow \]\[{{Q}_{2}}=\frac{{{Q}_{2}}}{{{T}_{1}}}\times {{Q}_{1}}=\frac{300}{900}\times 3\times {{10}^{6}}\] \[=1\times {{10}^{6}}\,\text{cal}\] work done \[={{Q}_{1}}-{{Q}_{2}}\] \[=3\times {{10}^{6}}-1\times {{10}^{6}}=2\times {{10}^{6}}\,\text{cal}\] \[=2\times 4.2\times {{10}^{6}}J=8.4\times {{10}^{6}}\,J\] Hence, the correction option is [b].
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