Question

An inventor claims to have devised a cyclical engine for use in space vehicles that operates with a nuclear fuel generated energy source whose temperature is 510 K and sink at 270 K that radiates waste heat to deep space. He also claims that this engine produces 4.1 kW while rejecting heat at a rate of 15,000 kJ/h. Is this claim valid?

Answer 1

Inventor claim is not valid.

Step-by-step explanation:

Given that

Source temperature = 510 K

Sink temperature = 270 K

Power produce = 4.1 KW

Heat reject = 15,000 KJ/h

Heat reject =4.16 KW

As we know that

Heat addition = Heat rejection + Power produce

Heat addition = 4.16 + 4.1 KW

Heat addition = 8.16 KW

So efficiency of engine

`\eta =(Power\ produces)/(heat\ added)`

`\eta =(4.1)/(8.16)`

`\eta =0.502`

Now check the maximum efficiency can be possible by using Carnot heat engine

As we know that efficiency of Carnot heat engine given as

`\eta =1-(T_L)/(T_H)`

By putting the value

`\eta =1-(T_L)/(T_H)`

`\eta =1-(270)/(510)`

`\eta =0.47`

So the efficiency of Carnot cycle is less than the efficiency of above given engine.So this engine is not possible.It means that inventor claim is not valid.