# Change of Entropy Problem

1. Apr 22, 2012

### jfislove

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

A 4.50 kg block of ice at 0 C falls into the ocean and melts. The average temperature of the ocean is 3.50 C, including all the deep water. By how much does the melting of this ice change the entropy of the world?

2. Relevant equations

Not sure if I should be using any equations as such, I've just been multiplying known values to get the energy, temperature and mass of the water and ice.

3. The attempt at a solution

I googled the mass of all water in the earth's oceans, and got a figure of 7.61x10^23 kg, so I multiplied the specific heat capacity of water (4190 J/kg.K) by this mass to try and get the entropy of all the water, so I got 3.19x10^23 J/K.

I then got the entropy of the ice block by multiplying the latent heat of fusion of ice (3.34x10^5 J/kg) by the mass of the block and dividing it by the absolute temperature of the ice (273.15 K), giving what I thought was the entropy of the block to be 5502.47 J/K.

Obviously, because the two numbers are on completely different scales, adding/subtracting them makes almost no difference to the answer, so I've really no idea how to handle the question from here on!!

All help is appreciated!

2. Apr 22, 2012

### George Jones

Staff Emeritus
Tw0 things happen to the water in the ice. First the ice melts, and then the water in the ice that melted changes temperature.

How is the entropy change for the second process calculated?

Does the temperature of the ocean change? From where does the energy come that melts the ice and raises its temperature?

3. Apr 22, 2012

### jfislove

"How is the entropy change for the second process calculated?"

Not sure how to calculate ANY entropy process, the textbook I have here (Sears and Zemansky's University Physics) gives me an equation dS = ∫dQ/T, where S is the entropy, Q is the heat energy and T is the absolute temperature, but I'm not sure how to apply that to what I have, I guess the ice block's temperature changes to the 3.5 C, but then where do I get the dQ value?

"Does the temperature of the ocean change? From where does the energy come that melts the ice and raises its temperature?"

I assume the temperature of the ocean drops SLIGHTLY, but I can't imagine it drops by any noticeable amount? Surely the energy comes from the slightly warmer ocean?

4. Apr 22, 2012

### George Jones

Staff Emeritus
From the definition of specific heat.