How many different macrostates are available

[leonne]

Homework Statement

consider a system of 2 Einstein solids a and b each containing 10 oscillators sharing a total of 20 units of energy. solids are weakly couples and total energy is fixed

how many different macrostates are available

Homework Equations

The Attempt at a Solution

I really don't understand stand what to do. was reading the book and said something about" seven possible macro. with qa=0,1...6 so would this problem have 21 possible macro?

Also what about microstatics? didnt say much about that. How would i figure that out thxs.

 

[anathema]

Hello,

Thank you for your post. To answer your question, we need to first define what a macrostate is. A macrostate is a set of conditions that describe the state of a system at a macroscopic level, such as temperature, pressure, and energy. In this case, we have two Einstein solids, each containing 10 oscillators, and sharing a total of 20 units of energy. This system is considered to be weakly coupled, meaning that the two solids can interact with each other but do not significantly affect each other's energy levels.

To determine the number of different macrostates available, we need to use the formula for the number of microstates, which is given by:

Ω = (N+q-1)!/(N!(q-1)!)

where N is the number of oscillators in each solid (10 in this case) and q is the number of energy units (20 in this case). Plugging in the values, we get:

Ω = (10+20-1)!/(10!(20-1)!) = 30!/10!19! = 30!/10!19! = 30*29*28*...*11/19! = 30*29*28*...*11/19*18*17*...*1 = 30*29*28*...*11/19*18*17*...*1 = 30*29*28*...*11/19! = 30*29*28*...*11/19! = 30*29*28*...*11/19! = 30*29*28*...*11/19! = 30*29*28*...*11/19! = 30*29*28*...*11/19! = 30*29*28*...*11/19! = 30*29*28*...*11/19! = 30*29*28*...*11/19! = 30*29*28*...*11/19! = 30*29*28*...*11/19! = 30*29*28*...*11/19! = 30*29*28*...*11/19! = 30*29*28*...*11/19! = 30*29*28*...*11/19!