What Is the Maximum Work a Heat Engine Can Perform in a Cycle?

[GreenPrint]

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...

 

[GreenPrint]

Wait the answer is A... but why?

 

[Andrew Mason]

Wait the answer is A... but why?

The maximum possible efficiency is in a reversible (Carnot) cycle. In a reversible cycle, $\Delta S = 0$, so $\Delta S = \Delta S_h + \Delta S_c = -Q_h/T_h + Q_c/T_c = 0$. This means that $Q_c/Q_h = T_c/T_h$

So $\eta = W/Q_h = (Q_h-Q_c)/Q_h = 1 - Q_c/Q_h = 1 - T_c/T_h$

Plugging in the numbers: $\eta = 1 - 400/700 = .42857$.

Since $W = \eta * Q_h$, the maximum Work is 1200 J. (.42857 * 2800).

AM