Finding exhaust temp in heat engine problem (entropy) (1 Viewer)

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1. The problem statement, all variables and given/known data

The question is: An ideal heat engine takes in heat Q(in) at a temp T(h). It exhausts heat Q(out). So: (a) how much work is done by engine (b) what is efficiency of engine (c) what is exhaust temp of engine and (d) calculate the answers to above for heat input of 460J at a temp of 600K and heat output of 285J.

2. Relevant equations

3. The attempt at a solution

So I have done so far:
(a) W = Qin - Qout
(b) E = W/Qin

but (c) is the bit that confuses me! so far I have got:
deltaS = deltaQ / T = (Qin - Qout) / T(h)

now after getting the above answer for deltaS, do I now rearrange it to get T = deltaS x deltaQ and plug that answer into this equation to get the final temp?

So to use the figures supplied would look like this:

deltaS = deltaQ / T

= (460 - 285)J / 600K = 0.29 JK (not sure what the unit is here?)

now plug into:

T = deltaS x deltaQ

= 0.29 x 175J

= 51.04 (again not sure what unit?)

I'm a bit lost here - am I on the right track or waaaaaay off???

Thanks heaps.


Staff Emeritus
Science Advisor
Homework Helper
(b) You're correct here, but they might want the answer expressed in terms of the given parameters Q(in), T(h), and/or Q(out)

(c) An "ideal heat engine" generally means one that uses the Carnot Cycle. Your text-book should have a formula for the efficiency of a Carnot Cycle engine, in terms of the temperatures Th and Tc.

If you find that, you can compare it with the usual expression,

E = W / Qin

and from there figure out what the exhaust temperature is.

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