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An inventor claims that he has developed an engine that produces 200 kW (d) power by receiving 225 kW heat from a source of 600 °C and rejecting the waste heat to a sink at 80°C. () Estimate the rejection heat and the thermal efficiency of the engine claimed. (ii) Is this a reasonable claim? Why?

Respuesta :

Answer:

[tex]Q_R=25 K W[/tex]

[tex]\eta = 0.88[/tex]

Explanation:

Given that

Power produces=200 KW

Power input=225 KW

We know that from first law of thermodynamics

[tex]Q_A = Q_R+W[/tex]

Where

[tex]Q_A[/tex] heat in put

[tex]Q_R[/tex] heat rejection

W is the power output

So now putting the values

[tex]225=200+Q_R[/tex]

[tex]Q_R = 25 KW [/tex]

We know that thermal efficiency given as

[tex]\eta = \dfrac{W}{Q_A}[/tex]

[tex]\eta = \dfrac{200}{225}[/tex]

[tex]\eta = 0.888[/tex]

Now to find the possibility of such type of engine .we will find the Carnot efficiency at given temperature and then will compare will obtain above efficiency of engine.

We know that  Carnot efficiency is the maximum possible efficiency of any type work producing devices.No any device will have efficiency more than Carnot efficiency .If any device will have more than Carnot efficiency then it device will not possible.

So Carnot efficiency

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

[tex]\eta_c = 1-\dfrac{353}{873}[/tex]

[tex]\eta_c =0.595 [/tex]

So this device is not possible because it have efficiency more than Carnot efficiency.This is not reasonable.

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