# How to calculate entropy for a system

1. Jun 15, 2012

### CraigH

How can you acuratley measure this? I cant see how you can give randomness a number? I've seen in some places that S = ln(the number of possible arangments) Is this true in all cases? But how can you measure the number of possible arangements?, it seems imposible to calculate the entropy for a complicated system.
Thanks

2. Jun 15, 2012

### Andrew Mason

The thermodynamic definition of entropy S at a temperature T is:

$S = \int_{0}^T dS + S_0 = \int_{0}^T \frac{dQ}{T} + S_0$

where S0 is the entropy at absolute zero which is not really defined but you can take it to be 0. Strictly speaking, it is only zero for molecular structures that can have only one microstate at absolute zero.

In order to calculate this integral, you just need to know the heat capacity of the substance as a function of temperature.

AM

Last edited: Jun 15, 2012