Equipartition Thm: mv_x^2/2 = k_B T/2

  • Thread starter Thread starter michael892
  • Start date Start date
  • Tags Tags
    Theorem
Click For Summary
The discussion focuses on demonstrating the equipartition theorem, specifically showing that the average kinetic energy in one dimension, represented as mv_x^2/2, equals k_B T/2. Participants suggest substituting the expression for the velocity distribution function ρ(v_x) into the integral. Calculating this integral is emphasized, with the recommendation to consult a table of integrals if needed. The goal is to establish the relationship between kinetic energy and temperature as outlined by the equipartition theorem. Successful completion of this calculation confirms the theorem's validity in the context of statistical mechanics.
michael892
Messages
3
Reaction score
0
show that
< \frac{mv_{x}^{2}}{2}> \equiv s\int_{-\infty }^{\infty} \frac{mv_{x}^{2}}{2} \rho (v_{x}) dv_{x}=\frac{k_{B}T}{2}

im stuck
 
Last edited:
Physics news on Phys.org
Plug in the expression for ρ(vx) inside the integral and then actually calculate the integral, or look it up in a table of integrals.
 
Thread 'What is the pressure of trapped air inside this tube?'

Thread 'What is the pressure of trapped air inside this tube?'

As you can see from the picture, i have an uneven U-shaped tube, sealed at the short end. I fill the tube with water and i seal it. So the short side is filled with water and the long side ends up containg water and trapped air. Now the tube is sealed on both sides and i turn it in such a way that the traped air moves at the short side. Are my claims about pressure in senarios A & B correct? What is the pressure for all points in senario C? (My question is basically coming from watching...
View full post »

Similar threads

MIT OCW 8.01 PS11.3: Elastic Collision Between Ball and Pivoted Rod
  • · Replies 10 ·
Replies
10
Views
3K
High School Helix in intrinsic coordinates?
  • · Replies 6 ·
Replies
6
Views
1K
Undergrad Some notes on stochastic physics
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Conservation Laws from Continuity Equations in Fluid Flow
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Integration of Poisson's Equation
  • · Replies 9 ·
Replies
9
Views
4K
Undergrad Power done by work on a continuous body isn't the derivative of work?
  • · Replies 11 ·
Replies
11
Views
2K
High School In uniform acceleration, mean velocity ##\bar v = \frac{v_0+v}{2}##?
  • · Replies 23 ·
Replies
23
Views
3K
Undergrad Deriving the time-dependent wave equation from Energy eigenfunctions
  • · Replies 1 ·
Replies
1
Views
1K
Graduate The equations of variable mass systems
  • · Replies 4 ·
Replies
4
Views
2K
Help understanding modal projection in PDE with assumed solution form
  • · Replies 4 ·
Replies
4
Views
1K