A Carnot engine having an efficiency of `eta = (1 / 10)` as a heat engine is used as a refrigerators. If the work done on the system is 10 J, what is the amount of energy absorbed from the reservoir at lowest temperature ?

Explanation

As heat engine, let Q the heat energy absorbed from the source and `Q_(2)` be the energy rejected to the sink. Then
`Q_(1)=W+Q_(2)=10+Q_(2)" …(1)"`
`"Given : "eta=1-(Q_(2))/(Q_(1))=(1)/(10)`
`(Q_(2))/(Q_(1))=1-(1)/(10)=(9)/(10)`
`Q_(1)=(10)/(9)Q_(2)" ...(2)"`
From equation (1) and (2),
`10+Q_(2)=(10)/(9)`
`10=((10)/(9)-1)Q_(2)`
`therefore" "Q_(2)=90J`