Question

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

e = |W|/|Qh|

|Qh| = |W| + |Ql|

e = 1 - |Ql|/|Qh|

Answer 1

wait no the answer is A how though?

Answer 2

In a maximum-efficiency "Carnot" cycle, the ratio
Qout/Qin = Tout/Tin
because the entropy change when heat is absorbed and released by the fluid is the same. T remains the same during each process.

Therefore e = 1 - Tout/Tin = 3/7, and
Wout = 3/7 * 2800 = 1200 J

Practical engines do not use a Carnot cycle, but come reasonably close.