Suppose that two heat engines are connected in series, such tha the heat exhaust of the first engine is used as the heat input of the second engine as shown in the figure. The efficiences of the enginess are `eta_(1)` and `eta_(2)`, respectively What will be net efficiency of the combination?

Options

A. `eta_("net")=eta_(2)+(1-eta_(1))eta_(2)`
B. `eta_("net")=(eta_(1))/((1-eta_(1))eta_(2))`
C. `eta_("net")=eta_(1)+(1-eta_(1))eta_(2)`
D. `eta_("net")=(1-eta_(1))/((1-eta_(2))eta_(2))`

Answer

C

Explanation

Suppose that `eta_(1)=(Q_(1)-Q_(2))/(Q_(1))=1-(Q_(2))/(Q_(1))`
`Q_(1)=(Q_(2))/(1-eta_(1))`
`eta_(2)=(Q_(2)-Q_(3))/(Q_(2))=1-(Q_(3))/(Q_(2))`
`Q_(3)=Q_(2)(1-eta_(2))`
Now `eta=(Q_(1)-Q_(3))/(Q_(1))=1-(Q_(3))/(Q_(1))`
`=1-(Q_(2)(1-eta_(2)))/(Q_(2))(1-eta_(1))`