A reversible engine takes in 2000J from a reservoir at 400K; it gives up Q1' J to a reservoir at 300K and Q1 J to a reservoir at 200K, doing 750J of work/cycle. Find Q1' and Q1.
So at first glance the relevant equation would seem to be the work equation W=Q2-Q1, however this wouldn't account for the difference in the two reservoir temperatures. So my next thought was to use the proportions Q1/Q2 = T1/T2.
The Attempt at a Solution
If I go with my gut and use the proportion what I get is:
Q1/Q2 = T1/T2
Q1/2000 = 300/400
Q1/2000 = 200/400
Q1 = 1000J
Now, I can tell almost by inspection that these results are way off (and indeed the book values give are 750J and 500J). If I attempt using the basic W = Q2-Q1, I get W = 1250, but again this doesn't account for temperature (but is conveniently the sum of the given answers).
What am I doing wrong? Any nudge in the right direction would be appreciated.