question_answer

An engine operates by taking n moles of an ideal gas through the cycle ABCDA shown in figure. The thermal efficiency of the engine is - (Take \[{{C}_{v}}=1.4R,\]where R is gas constant)                                             [JEE Online 08-04-2017]

A)  0.24    

B)       0.15

C)  0.32                 D)       0.08 Correct Answer: B Solution : [b] \[w={{P}_{0}}{{V}_{0}}\]

Heat given \[={{Q}_{AB}}={{Q}_{BC}}\]

\[=n{{C}_{V}}d{{T}_{AB}}+m{{C}_{P}}d{{T}_{BC}}\]

\[=\frac{3}{2}(nR{{T}_{B}}-nR{{T}_{A}})+\frac{5}{2}(nR{{T}_{C}}-nR{{T}_{B}})\]

\[=\frac{3}{2}(2{{P}_{0}}{{V}_{0}}-{{P}_{0}}{{V}_{0}})+\frac{5}{2}(4{{P}_{0}}{{V}_{0}}-2{{P}_{0}}V)\]

\[=\frac{13}{2}{{P}_{0}}{{V}_{0}}\]

\[n=\frac{\text{w}}{\text{Qgiven}}=\frac{2}{13}=0.15\]