# Entropy of a system?

1. Jun 15, 2006

### pivoxa15

What would you do if you were asked to calculate the entropy of an object such as an apple? Does the question even make sense?

2. Jun 15, 2006

### pivoxa15

If it makes sense. What does it mean?

3. Jun 15, 2006

### Tzemach

In accordance with the second law of entropy the apple would move from order to disorder, which simply means that eventually it will go rotten.

4. Jun 16, 2006

### Romperstomper

It makes sense. What it means is taking the natural log of the multiplicity(the number of way of arranging things in the system) multiplied by Boltzmann's constant. S = k*ln(omega)

The second law of thermodynamics says that this number tends to increase. So like Tzemach said, the apple will rot.

Last edited by a moderator: Jun 16, 2006
5. Jun 16, 2006

### vanesch

Staff Emeritus
Well, you'd have to count all the different microscopic arrangements of the particles in the apple which would still be compatible with your description of "apple". This number, N, is then entered in Boltzman's formula:

S = k ln N

with k = Boltzmann's constant, and it will give you the entropy.
k = 1.38 10^(-23) Joule/Kelvin

As you see, the concept of entropy is in principle dependent of the precision by which you describe your apple, but this is usually taken as "macroscopically distinct" descriptions. And, when you look at it numerically, it really doesn't change much the value of S when you add, or leave out, an extra macroscopic specification.
This is because even if your macroscopic description changes the number N of compatible states, by, say, a factor 10^50, this would only change your entropy by k x ln 10^50 ~ k x 150 ~ 10^(-20) Joule/Kelvin, an utterly small amount of entropy.

6. Jun 16, 2006

### Bystander

Or, you skip the stat mech, stick to old-fashioned, "smash-mouth" thermo, and integrate C/T from absolute zero to room T; or, add the third law entropies for 130-140 grams of water, 50-60 grams of sugars, and other organic compounds, plus an entropy of mixing term (sum of R(xlnx)), where x = mole fraction), and go on your merry way.

7. Jun 19, 2006

### lalbatros

And what about burning it in a lab?
Could the measurement of the combustion product allow backflushing to the entropy of the apple?