# Boltzmanns entropy equation

by cnidocyte
Tags: boltzmanns, entropy, equation
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P: 36
In my textbook they claim that:
 Each thermodynamic state has a characteristic number of microstates associated with it, and we use the symbol W for this number.
They lost me when they said "thermodynamic state". Do they mean thermodynamic system? I know that a system such as a container of gas will have a very large number of microstates considering the amount of gas molecules present and that statistical methods would be required to calculate the number of microstates. I know that a system like this also has macrostates such as pressure, volume, temperature etc. but I don't know what they mean when they say a thermodynamic "state" has a number of microstates associated with it. To add to my confusion, a bit further down they say:
 Thus, entropy is a measure of how many microstates are associated with a particular macroscopic state.
What macroscopic states are they talking about here? Are they saying macrostates like pressure or volume have microstates associated with them?
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 Quote by cnidocyte In my textbook they claim that: They lost me when they said "thermodynamic state". Do they mean thermodynamic system? I know that a system such as a container of gas will have a very large number of microstates considering the amount of gas molecules present and that statistical methods would be required to calculate the number of microstates. I know that a system like this also has macrostates such as pressure, volume, temperature etc. but I don't know what they mean when they say a thermodynamic "state" has a number of microstates associated with it.
The thermodynamic state refers to a set of macroscopically measured parameters of a substance in thermal equilibrium. Any other system in thermal equilibrium having those same parameters will be thermodynamically "the same".

For an ideal gas, the thermodynamic state is defined by Pressure, Volume and Temperature. Any other ideal gas at the same Pressure, Volume and Temperature will be thermodynamically equivalent.

For a paramagnetic system, magnetic intensity and magnetization as well as pressure, volume and temperature define the thermodynamic state.

A thermodynamic system may consist of different components that are in thermal equilibrium with themselves but are not in thermal equilibrium with each other. So a thermodynamic system may not have a single thermodynamic state.
 What macroscopic states are they talking about here? Are they saying macrostates like pressure or volume have microstates associated with them?
Even a small quantity of an ideal gas (in thermal equilbrium) consists of a huge number of molecules all moving in different directions and speeds. The microstate describes the motions of all the molecules. Two samples of an ideal gas having the same parameters of P, V and T will not have the same microstates (ie their molecules are not all moving identically at any given time). Indeed, the microstates of each sample are continually changing. However, since their thermodynamic parameters remain unchanged, for thermodynamic purposes, they are the same.

AM
 P: 36 Thanks a lot!

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