Temperature in a Carnot heat engine

[EightBells]

Homework Statement

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?

Homework Equations

η=1-(Tc/Th)=W/Qh

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'.

 

[vela]

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 $W$?

 

[EightBells]

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 $W$?

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

Plug that into W/Qh=1-(Tc/Th) and Th=494 K=221°CThat's the correct answer, thanks so much!