How to calculate entropy for a system

[CraigH]

How can you acuratley measure this? I can't 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

 

[Andrew Mason]

How can you acuratley measure this? I can't 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 impossible to calculate the entropy for a complicated system.
Thanks

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