Heat Engine Cycle Question

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Homework Statement



21. A heat engine operates in a cycle between temperatures 700 K and 400 K. The heat input to the engine during each cycle is 2800 J. What is the maximum possible work done by the engine in each cycle?

(A) 1200 J
(B) 1600 J
(C) 2100 J
(D) 2800 J
(E) 4400 J

I believe that the answer is E. I just don't know how to prove it. If you could show that would be great. I know that



Homework Equations



e = |W|/|Qh|

|Qh| = |W| + |Ql|

e = 1 - |Ql|/|Qh|

The Attempt at a Solution



I'm lost...

e = |W|/|Qh|

|Qh| = |W| + |Ql|

e = 1 - |Ql|/|Qh|

I don't remember how to do this type of problem...
 

Answers and Replies

  • #2
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Wait the answer is A... but why?
 
  • #3
Andrew Mason
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Wait the answer is A... but why?
The maximum possible efficiency is in a reversible (Carnot) cycle. In a reversible cycle, [itex]\Delta S = 0[/itex], so [itex]\Delta S = \Delta S_h + \Delta S_c = -Q_h/T_h + Q_c/T_c = 0[/itex]. This means that [itex]Q_c/Q_h = T_c/T_h[/itex]

So [itex]\eta = W/Q_h = (Q_h-Q_c)/Q_h = 1 - Q_c/Q_h = 1 - T_c/T_h[/itex]

Plugging in the numbers: [itex]\eta = 1 - 400/700 = .42857[/itex].

Since [itex]W = \eta * Q_h[/itex], the maximum Work is 1200 J. (.42857 * 2800).

AM
 

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