# Heat Engine Cycle Question

## 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...

Wait the answer is A... but why?

Andrew Mason
Homework Helper
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