How to calculate entropy for a system

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Accurately measuring randomness and entropy in complex systems poses significant challenges, particularly in calculating the number of possible arrangements. The formula S = ln(number of possible arrangements) is cited as a method for determining entropy, but its applicability can vary based on the system's complexity. The thermodynamic definition of entropy involves integrating heat capacity over temperature, which requires knowledge of the substance's heat capacity function. While calculating entropy can be straightforward for simple systems, it becomes increasingly difficult for more complicated ones. Understanding these principles is crucial for accurately assessing entropy in various contexts.
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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
 
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CraigH said:
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
 
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