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So I read some introductory concepts in my textbook and watched two Khan Academy videos:

https://www.youtube.com/watch?v=5EU-y1VF7g4

https://www.youtube.com/watch?v=lKq-10ysDb4

I would like to clear something up which i am confused about:

So if the system is in thermodynamic equilibrium, the macrostates such as pressure, temperature etc are well defined.

Does this mean that they are constant throughout the given system. So if I say the pressure is 5 Bar, its 5 Bar everywhere (and ignoring hydrostatic variation? If we included hydrostatic variation, such as looking at the ocean as a system, does that mean the pressure is not "well defined"?

My understanding of a state is that it is a system with enough (by the state postulate) well defined macrostates* to describe it. So does that mean in the case of an ocean, we cannot describe it as a "state"?

Also, for quasi-static equilibrium processes, if we did NOT make this assumption, lets say at the beginning and end of a process, could we describe these as "states" because they have well defined macrostates but in between, would we need to use, say, fluid dynamics, instead of classical thermodynamics, to describe the process?

*(I am aware microstates are always "well defined" - but I think this is used for statistical thermo and not classical thermo of which I am asking about and must obviously learn first).
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Desk-Lamp
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You have to be a bit careful about what you mean by 'classical' and statistical thermodynamics- the concept of a microstate is one that only really applies to statistical mechanics. As far as old school thermodynamics is concerned,the system is only defined by the easily measurable quantites, Temperature Pressure etc., which you're referring to as macrostates. In a modern physics course there isn't really any need to do 'classical' thermodynamics at all, but it tends to be taught a bit alongside statistical mechanics because some people find it easier to grasp intuitively.

In an attempt to answer your questions: A quantity like temperature is determined for a system as a whole, so you can't say anything about variation within a system. If you wanted to calculate this sort of stuff for a big complicated system like the ocean, what you'd essentially do is work out the physics for a simple system (i.e. a cube of water), and then consider the ocean as a massive set of those interacting smaller systems. Obviously by that point you're not really doing statistical mechanics anymore.

I think most of this will become clear if you think very carefully about what you mean by a state.
A microstate is the exact description of the system, so the exact state of every particle and object in the system. When you look at something like a gas there's no way to know the exact microstate, so you measure a macroscopic quantity like the energy, and say that the system's in the macrostate with that energy. What you're saying by that is that we know the system is in one of the microstates with that energy but we don't know (or care)which one.

Apoogy for wall of text :/
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uberteknik
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(Original post by Desk-Lamp)
You have to be a bit careful about what you mean by 'classical' and statistical thermodynamics- the concept of a microstate is one that only really applies to statistical mechanics. As far as old school thermodynamics is concerned,the system is only defined by the easily measurable quantites, Temperature Pressure etc., which you're referring to as macrostates. In a modern physics course there isn't really any need to do 'classical' thermodynamics at all, but it tends to be taught a bit alongside statistical mechanics because some people find it easier to grasp intuitively.

In an attempt to answer your questions: A quantity like temperature is determined for a system as a whole, so you can't say anything about variation within a system. If you wanted to calculate this sort of stuff for a big complicated system like the ocean, what you'd essentially do is work out the physics for a simple system (i.e. a cube of water), and then consider the ocean as a massive set of those interacting smaller systems. Obviously by that point you're not really doing statistical mechanics anymore.

I think most of this will become clear if you think very carefully about what you mean by a state.
A microstate is the exact description of the system, so the exact state of every particle and object in the system. When you look at something like a gas there's no way to know the exact microstate, so you measure a macroscopic quantity like the energy, and say that the system's in the macrostate with that energy. What you're saying by that is that we know the system is in one of the microstates with that energy but we don't know (or care)which one.

Apoogy for wall of text :/
Nice description, thank you.

An example of an application with variation in the system is weather modelling where Finite Element Analysis of individual smallish (10x106 m3) 'cubes' of air and ocean are individually treated as bounded-macrostates, with net energy inflow and outflow between adjacent cubes at discrete time intervals collectively treated as the system-macrostate.

Other examples of this technique are applied in 3D to stress analysis, liquid and gas flow dynamics, electromagnetic fields, current density etc.
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