# Melting Ice with a Carnot Engine

1. Dec 12, 2007

### xinlan

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

A Carnot heat engine uses a hot reservoir consisting of a large amount of boiling water and a cold reservoir consisting of a large tub of ice and water. In 5 minutes of operation of the engine, the heat rejected by the engine melts a mass of ice equal to 3.50×10−2 kg .

Throughout this problem use Lf = 3.34*10^5 J/kg for the heat of fusion for water.

During this time, how much work W is performed by the engine?

2. Relevant equations

W = Q-ΔEint

3. The attempt at a solution

I calculated Q = M * Lf
3.50*10^-2 * 3.34*10^5 = 11690 J

then I don't know what to do..
please help me..

thanks in advance

2. Dec 13, 2007

### dynamicsolo

The clue is in this sentence. The amounts of each form of water is large so that heat transfer does not cause their temperatures to change significantly. What are those temperatures? You will need them in order to calculate the efficiency e_c of this Carnot engine. Knowing that efficiency, you can now say that

e_c = W_net / Q_input .

What you have computed here

Q = M * Lf = 3.50*10^-2 * 3.34*10^5 = 11690 J

is the heat output (since it was used to melt some of the ice). You know from conservation of energy that

Q_input = W_net + Q_output .

So you should have everything you need to find W_net.

Last edited: Dec 13, 2007
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