What Are the Microstates Associated with a Thermodynamic State?

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In summary: I was a little lost after they said "thermodynamic state" and I didn't understand what they were trying to say. They lost me again when they said "macroscopic state" because I don't know what that is either. In summary, a thermodynamic state refers to a set of macroscopically measured parameters of a substance in thermal equilibrium. Two samples of an ideal gas having the same parameters of P, V and T will not have the same microstates, but their thermodynamic parameters remain unchanged for thermodynamic purposes.
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cnidocyte
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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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  • #2
cnidocyte said:
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
 
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Thanks a lot!
 

What is Boltzmann's entropy equation?

Boltzmann's entropy equation is a mathematical formula that describes the relationship between a system's microstates (possible arrangements of particles) and its macrostate (observable properties such as temperature and pressure). It is represented as S = k ln(W), where S is the entropy, k is Boltzmann's constant, and W is the number of microstates.

How is Boltzmann's entropy equation used in thermodynamics?

In thermodynamics, Boltzmann's entropy equation is used to calculate the entropy of a system and predict the direction of spontaneous processes. It helps to explain the tendency of systems to become more disordered over time, as described by the Second Law of Thermodynamics.

What is the significance of Boltzmann's constant in the entropy equation?

Boltzmann's constant, denoted as k, is a fundamental constant in physics that relates the macroscopic properties of a system to the behavior of its individual particles. In Boltzmann's entropy equation, k serves as a conversion factor between the microscopic and macroscopic scales, allowing for the calculation of entropy in terms of microstates.

How does Boltzmann's entropy equation relate to the concept of disorder?

Boltzmann's entropy equation states that the entropy of a system increases as the number of possible microstates increases. This means that as a system becomes more disordered (i.e. has more possible arrangements of particles), its entropy increases. Therefore, Boltzmann's entropy equation provides a mathematical explanation for the Second Law of Thermodynamics, which states that the entropy of a closed system always increases over time.

What are some real-world applications of Boltzmann's entropy equation?

Boltzmann's entropy equation has various applications in fields such as physics, chemistry, and biology. It is used to explain phenomena such as heat transfer, chemical reactions, and protein folding. Additionally, it has practical applications in fields such as engineering, where it is used to design more efficient systems and processes.

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