Finding exhaust temp in heat engine problem (entropy)

[aussie-girl]

Homework Statement

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.

Homework Equations

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.

 

[Redbelly98]

(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.

 

[nlightner]

I would like to clarify that the exhaust temperature of an ideal heat engine cannot be calculated using only the given information. The efficiency of an ideal heat engine is defined as the ratio of the work output to the heat input, and it is given by the equation E = 1 - Qout/Qin. In order to calculate the exhaust temperature, we would need to know the specific heat capacity of the working fluid and the temperature at which the heat is rejected. Without this information, it is not possible to determine the exhaust temperature. Additionally, the units for entropy are J/K, and the units for temperature are K. I would suggest reviewing the thermodynamic principles and equations for heat engines to better understand the problem and how to approach it.