A) \[\frac{2}{3}Q\]
B) \[\frac{3}{5}Q\]
C) \[\frac{2}{5}Q\]
D) \[\frac{1}{5}Q\]
Correct Answer: C
Solution :
\[\Delta Q=\Delta U+\Delta W\] \[\Rightarrow \]\[\Delta W={{(\Delta Q)}_{P}}-\Delta U={{(\Delta Q)}_{P}}\left[ \frac{1-{{(\Delta Q)}_{V}}}{{{(\Delta Q)}_{P}}} \right]\] \[={{(\Delta Q)}_{P}}\left[ 1-\frac{{{C}_{V}}}{{{C}_{P}}} \right]=Q=\left[ 1-\frac{3}{5} \right]=\frac{2}{5}Q\] \[\because \]\[{{(\Delta Q)}_{P}}=Q\]and \[\gamma =\frac{5}{3}\]for monatomic gas
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