How Many Basic States Exist for Particles in Divided Spaces?

AI Thread Summary
The discussion revolves around determining the number of basic states for four distinguishable particles in a room divided into octants. A basic state is defined as a unique configuration that specifies the location of each particle within the octants. Initially, participants express confusion about the concept of basic states and their relation to microstates and macrostates. The conversation clarifies that a basic state encompasses all possible configurations of the particles in the system. The problem also raises a question about how the number of basic states changes when the space is doubled by opening a door to an adjacent room.
Galactium
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Homework Statement


Four distinguishable particles move freely in a room divided into octants (there are no actual partitions). Let the basic states be given by specifying the octant in which each particle is located.

1. How many basic states are there?
2. The door to this room is opened, allowing the particles to move into an adjacent, identical room, also divided into octants. Now that the amount of space that can be occupied has been doubled, by what factor has the number of basic states increased?

Homework Equations


Ω=M^N ?[/B]

The Attempt at a Solution


Honestly, I do not even know how to start this problem. I have read the Mazur chapter 19 Entropy, but I still do not quite understand it.
 
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So let us start by understading the question. What would you say that a basic state is?
 
Orodruin said:
So let us start by understading the question. What would you say that a basic state is?
A basic state, also know as Microstate, is amount of distinguishable particles in a system. Whereas the Macrostate is in a larger scale in describing it by its properties, volume, pressure, temperature, etc.
 
Galactium said:
A basic state, also know as Microstate, is amount of distinguishable particles in a system
No, this is not correct. A basic state is a possible configuration that completely describes all the particles in the system.
 

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