What is the relationship between volume, spacing of energy levels, and entropy?

  • Context: Graduate 
  • Thread starter Thread starter weng cheong
  • Start date Start date
  • Tags Tags
    Energy Energy level
Click For Summary

Discussion Overview

The discussion centers around the relationship between volume, spacing of energy levels, and entropy, particularly in the context of quantum mechanics. Participants explore how changes in volume may affect the spacing of energy levels and, consequently, the entropy of a system.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant notes that entropy increases with the number of accessible energy levels (microstates) and suggests that increasing volume can decrease the spacing between these energy levels.
  • Another participant clarifies that the energy levels in question pertain to a quantum mechanical particle in a box, indicating that this relationship can be derived from quantum mechanics.
  • A participant inquires whether studying quantum mechanics is necessary to understand the derivation of the energy level equation.
  • It is affirmed that a non-quantum mechanical derivation is not known to one participant.
  • One participant provides a technical explanation involving the relationship between energy, momentum, and the quantization of wavenumber, stating that energy spacing is inversely proportional to the square of the box length (L).

Areas of Agreement / Disagreement

Participants generally agree on the quantum mechanical framework for understanding energy levels, but there is no consensus on the necessity of studying quantum mechanics for derivation or on the implications of volume changes on energy levels and entropy.

Contextual Notes

The discussion does not resolve the specific assumptions regarding the relationship between volume and energy level spacing, nor does it clarify the implications for entropy in detail.

Who May Find This Useful

Students and individuals interested in quantum mechanics, thermodynamics, and the relationship between entropy and energy levels may find this discussion relevant.

weng cheong
Messages
22
Reaction score
0
currently I'm studying the topic entropy. According to my text, entropy will increase when the accessible energy levels (microstates) increase. One of the approach to achieve this, we can decrease the spacing between energy levels by increasing the volume of the system.

i'm confused with this idea, i need a more detailed explanation on the change in spacing between energy level.
 
Science news on Phys.org
i'm still a pre-U student, so if i would like to know the derivation of the equation for energy level, i have to study quantum mechanics?
 
Yes. At least, I am not aware of a non-quantum mechanical derivation.
 
thanks a lot =)
 
Just consider a particle in a box. Energy is H=p^2/2, but momentum is related to wavenumber, which is quantized by the boundary condition that the wavefunction vanishes at the edge. So allowed momentum is related to L by p_n=n\hbar/L. So energy spacing is inversely proportional to L^2.
 

Similar threads

  • · Replies 6 ·
Replies
6
Views
4K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 39 ·
2
Replies
39
Views
7K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 5 ·
Replies
5
Views
1K
  • · Replies 4 ·
Replies
4
Views
5K