# Heat Engine Question

1. Nov 6, 2008

### joker_900

1. The problem statement, all variables and given/known data
Three identical bodies of constant thermal capacity are at temperatures 300 K, 300 K
and 100 K. If no work or heat is supplied from outside, what is the highest temperature
to which any one of these bodies can be raised by the operation of heat engines?

2. Relevant equations

3. The attempt at a solution

I don't think I'm on the right lines at all. Apparently I am supposed to get a cubic equation to solve, so I think I have approached this all wrong. But here's what I did:

So I thought the highest temperature would be achieved by using one of the 300K and the 100K as a heat engine, and using the work from that to pump heat from that same 100K to the other 300K.

I set up expressions of the form dQ = CdT for net heat energy entering each reservoir, to find the total heat energy that enters each body throughout the whole process. I also did conservation of energy and related work out of engine = work into pump.

I said that the whole process stops when the first 300K body and the 100K body reach the same temperature, Tf, as then the engine stops and there is no more energy in to pump heat.

I got: TH = T3i - 2Tf + T2i + T1i

where TH is the final temperature of the heated 300K body, Tji initial values 300K, 100K, 300K.

???

Thanks