A) \[\frac{2}{3}Q\]
B) \[\frac{3}{5}Q\]
C) \[\frac{2}{5}Q\]
D) \[\frac{1}{5}Q\]
Correct Answer: C
Solution :
Key Idea: Apply first law of thermodynamic In isobaric process \[Q=n{{C}_{P}}\Delta T\] Also, \[dU=n{{C}_{V}}\Delta T\] \[\therefore \] \[\frac{Q}{dU}=\frac{n{{C}_{P}}\Delta T}{n{{C}_{V}}\Delta T}=\frac{{{C}_{P}}}{{{C}_{V}}}=\gamma \] For monoatomic gas, \[\gamma =\frac{5}{3}\] \[\therefore \] \[\frac{Q}{dU}=\frac{5}{3}\] \[\Rightarrow \] \[dU=\frac{3}{5}Q\] Now, form first law of thermodynamics \[Q=dU+W\] \[\Rightarrow \] \[W=Q-dU\] \[=Q-\frac{3}{5}Q\] \[\therefore \] \[W=\frac{2}{5}Q\]
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