Deriving boltzmann distribution

  • #1
6
0
I was reading the derivation of boltzmann distribution using the reservoir model.
lets call the reservoir by index R and the tiny system by index A.
In the derivation they proposed that the probability for being at energy e (for A) is proportional to the number of states in reservoir. I didn't understand this completely and i would be happy to get some help!
here is my take on it, and please correct me if I'm wrong.
- The temperature of the whole system is T and it's constant therefor the number of states for the whole systems g is also constant
- both A and R are independent of each other therefor g = gA ⋅ gR
- if gR goes up then gA has to go down meaning gA ∝ gR
- P(e) ∝ 1/gA → P(e) ∝ gR
I'm not really convinced by my explanation so if someone could explain it and perhaps give me an intuitive physical explanation, I'd be happy. Thank you
 

Answers and Replies

  • #2
DrClaude
Mentor
7,428
3,702
The starting point is that all microstates are equally probable. Then if the system A is made up a single particle, its state has no influence on the total probability of the state of A + R (the multiplicity of A is always 1), so you can focus on the states of the reservoir only.
 

Related Threads on Deriving boltzmann distribution

Replies
2
Views
2K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
2
Views
993
  • Last Post
Replies
1
Views
5K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
4
Views
2K
Replies
1
Views
580
  • Last Post
Replies
2
Views
845
Replies
4
Views
6K
Top