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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?

Respuesta :

Answer:

Inventor claim is not valid.

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

[tex]\eta =\dfrac{Power\ produces}{heat\ added}[/tex]

[tex]\eta =\dfrac{4.1}{8.16}[/tex]

[tex]\eta =0.502[/tex]

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

As we know that efficiency of Carnot heat engine given as

[tex]\eta =1-\dfrac{T_L}{T_H}[/tex]

By putting the value

[tex]\eta =1-\dfrac{T_L}{T_H}[/tex]

[tex]\eta =1-\dfrac{270}{510}[/tex]

[tex]\eta =0.47[/tex]

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.

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