Question

An inventor claims to have devised a cyclical power engine that operates with a fuel whose temperature is 750 °C and radiates waste heat to a sink at 0 °C. He also claims that this engine produces 3.3 kW while rejecting heat at a rate of 4.4 kW. Is this claim valid?

Answer 1

Yes

Step-by-step explanation:

Given Data

Temprature of source=750°c=1023k

Temprature of sink =0°c=273k

Work produced=3.3KW

Heat Rejected=4.4KW

Efficiency of heat engine(η)=
`(Work produced)/(Heat supplied)`

and

Heat Supplied
`{\left (Q_s\right)}=Work Produced(W)+Heat rejected\left ( Q_r \right )`

`{Q_s}=3.3+4.4=7.7KW`

η=
`(3.3)/(7.7)`

η=42.85%

Also the maximum efficiency of a heat engine operating between two different Tempratures i.e. Source & Sink

η=1-
`\frac{T_ {sink}}{T_ {source}}`

η=1-
`(273)/(1023)`

η=73.31%

Therefore our Engine Efficiency is less than the maximum efficiency hence the given claim is valid.