Thank you for reporting, we will resolve it shortly
Q.
An engine operates by taking a monatomic ideal gas through the cycle shown in the figure. The percentage efficiency of the engine is close to ________.
$W _{ ABCDA }=2 P _{0} V _{0}$
$Q _{\text{ in }}= Q _{ AB }+ Q _{ BC }$
$Q _{ AB }= nC \left( T _{ B }- T _{ A }\right)$
$=\frac{ n 3 R }{2}\left( T _{ B }- T _{ A }\right)$
$=\frac{3}{2}\left( P _{ B } V _{ B }- P _{ A } V _{ A }\right)$
$=\frac{3}{2}\left(3 P _{ B } V _{0}= P _{0} V _{0}\right)=3 P _{0} V _{0}$
$Q _{ BC }= n C _{ P }\left( T _{ C }- T _{ B }\right)$
$=\frac{ n 5 R }{2}\left( T _{ C }- T _{ B }\right)$
$=\frac{5}{2}\left( P _{ C } V _{ C }- P _{ B } V _{ B }\right)$
$=\frac{5}{2}\left(6 P _{0} V _{0}-3 P _{0} V _{0}\right)=\frac{15}{2} P _{0} V _{0}$
$\eta=\frac{W}{Q_{\text {in }}} \times 100=\frac{2 P_{0} V_{0}}{3 P_{0} V_{0}+\frac{15}{2} P_{0} V_{0}} \times 100$
$\eta=\frac{400}{21}=19.04 \approx 19$
$\eta=19$
