# Homework Help: Temperature in a Carnot heat engine

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1. Apr 16, 2017

### EightBells

1. The problem statement, all variables and given/known data
A Carnot heat engine takes 95 cycles to lift a 10 kg. mass a height of 11 m . The engine exhausts 14 J of heat per cycle to a cold reservoir at 0∘C.

What is the temperature of the hot reservoir?

2. Relevant equations
η=1-(Tc/Th)=W/Qh
3. The attempt at a solution
I've tried: (Energy to lift mass)/(number of cycles)=W, so (mgh)/95=((10kg)(9.8m/s^2)(11m))/95= W=11.35 J/cycle
∴ 1-(Tc/Th)=11.35/14, so Tc/Th=1-(11.35/14), Th=Tc/(1-(11.35/14))=273 K/(1-(11.35/14))=1440 K=1170°C

This is an incorrect answer, and logically it seems too high.

I also considered where the 14 J/cycle exhausted to the cold reservoir is the work out, but then I don't know how to calculate Qh so that I'd only have one variable in the equation listed under 'Relevant Equations'.

2. Apr 16, 2017

### vela

Staff Emeritus
The problem statement says 14 J is the heat exhausted to the cold reservoir, so it's $Q_\text{C}$, not $Q_\text{H}$. You calculated $W$ correctly. How do you get $Q_\text{H}$ from $Q_\text{C}$ and $W$?

3. Apr 16, 2017

### EightBells

Qh=W+Qc=11.35+14=25.35 J/cycle

Plug that into W/Qh=1-(Tc/Th) and Th=494 K=221°C

That's the correct answer, thanks so much!!