Question

An ideal gas is subjected to cyclic process involving four thermodynamics thates, the amounts of heat `(Q)` and work `(W)` involved in each of these states.
`Q_1=6000J,Q_2=-5500J,Q_3=-3000J,Q_4=3500J`
`W_1=2500J,W_2=-1000J,W_3=-1200J,W_4=xJ` The ratio of the net work done by the gas to the total heat absorbed by the gas is `eta`. The values of x and `eta` respectively are
A. `500,7.5%`
B. `700,10.5%`
C. `1000,21%`
D. `1500,15%`

Answer 1

Correct Answer - B
In cyclic process
`Q_1+Q_2+Q_3+Q_4=W_1+W_2+W_3+W_4`
`6000-5500-3000+3500=2500-1000-1200+x`
`x=700J`
`DeltaQ_(cyclic)=DeltaW_(cyclic)=1000J`
`eta=(DeltaW_("cyclic"))/("Heat supplied")=(1000)/(Q_1+Q_4)=(1000)/(6000+3500)`
`=(10)/(95)=(2)/(19)` i.e., `(200)/(19)=10.5%`