1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Temperature as a function of vibration energy quanta

  1. Nov 30, 2016 #1
    1. The problem statement, all variables and given/known data
    Consider a small cluster of four copper atoms. Assume, that each atom can oscillate around its equilibrium position independently of the other atoms. Let us model each direction of vibration as a harmonic oscillator, whose energy is quantized
    Evib = ¯hω(n +1/2), where ω = sqrt(k/m), k is the ’spring constant’ of the bond between the atoms (k ≈ 120 N/m) and m is the mass of the copper atom. Compute as the function of vibration energy quanta n = 0,1,2,3,... the (a) number of microstates Ω
    (b) entropy S
    (c) temperature T
    (d) heat capacity C / atom

    2. Relevant equations


    3. The attempt at a solution
    I have already functions for the number of microstates and the entropy S:
    Ω(n) = ((n+11)!) : (n!11!)
    S(n) = k*ln (((n+11)!) : (n!11!)
    Now I try to find the function T(n) and started with:

    1/T = dS/dEint (dS = change in entropy, dEint = change in internal energy)

    Can I put this equations as T = dEint/dS ?
     
  2. jcsd
  3. Dec 4, 2016 #2
    Yes you can do that, but you'll have to put E(int) in terms of S. It may help if you're allowed to make the assumption that n >> # of oscillators.
     
    Last edited: Dec 4, 2016
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Temperature as a function of vibration energy quanta
  1. Energy and temperature (Replies: 12)

Loading...