An ideal monoatomic gas `(gamma=(5)/(3))` goes through a cyclic process consisting two isochoric and two isobaric lines. The absolute temperature of the gas rises two times both in isochoric heating and isobaric expansion. If number of moles are three, find efficiency of cyclic process.

Explanation

First sketch the process on `P-V` diagram.
Let initial thermodynamic coordinates are `(P_0,V_0,T_0)`
`DeltaW_(cyclic)=P_0V_0=3RT_0`
`DeltaQ_(1rarr2)=nC_V(T_2-T_1)=3.(3R)/(2)(2T_0-T_0)=(9RT)/(2)`
`DeltaQ_(2rarr3)=nC_P=(T_3-T_2)=3.(5R)/(2)(4T_0-2T_0)`
`=15RT_0`
`DeltaQ_(3rarr4)=-ve`,`DeltaQ_(4rarr1)=-ve`
Efficiency `eta=(DeltaW_(cyclic))/("Heat supplied")=(DeltaW_(cyclic))/(DeltaQ_(1rarr2)+DeltaQ_(2rarr3))`
`=(3RT_0)/((9)/(2)RT_0+15RT_0)=(6)/(39)=(2)/(13)`
`eta=(2)/(13)xx100=(200)/(13)%`