A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Frostbite

  • one year ago

Thermodynamics, statistical thermodynamics and spectroscopy COMBINED!

  • This Question is Closed
  1. Frostbite
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    The electronic ground state of the Cl atom is fourfold degenerate, while the first electronically excited state is doubly degenerate and lies 881 cm–1 above the ground state. Calculate the contribution to the molar heat capacity at constant volume, \(C_{V,m}(T)\) of Cl atoms from electronic states at 500 Kelvin. There are two alternative ways solving this problem :)

  2. Frostbite
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    (answer should include some theory why) ;)

  3. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Off the top of my head the only thing I think I am looking at is the energy difference given in wave numbers, so I have \[E = h c \tilde\nu\] And then I believe, not entirely sure: \[\left( \frac{\partial U}{\partial T} \right)_V = C_V\]

  4. Frostbite
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Yup, just need to evaluate the derivative and you are almost there :)

  5. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    It looks like from your notes you gave me that \[C_v = \frac{N \sigma^2}{kT}\] However it's at about this time during the day that it's my bedtime. I've been awake for a while so I'll have to come back and finish this tomorrow. :)

  6. Frostbite
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Yeah, I can see the notes somewhat is lacking in terms of the Boltzmann distribution to make it clear HOW to find the variance. So I make this an worked example: The average energy must be the sum of the energy multiplied with probability of finding the specie with the energy: \[\Large \langle \epsilon \rangle=\sum_{i}^{}p_i \epsilon_i\] The Boltzmann distribution allows us to calculate the probability of finding a specie with the energy \(\large \epsilon_i\): \[\Large p_i=\frac{ e^{- \beta \epsilon_i} }{ q }\] Where \(q\) is the partition function: \[\Large q=\sum_{\sf states~i}^{}e ^{- \beta \epsilon_i}=\sum_{\sf levels~i}^{}g_ie ^{- \beta \epsilon_i}\] Where \(g_i\) is the degeneracy of the ith energy level. The average energy is can therefor be written as: \[\Large \langle \epsilon \rangle=\sum_{i}^{}p_i \epsilon_i=\sum_{i}^{}\frac{ e ^{- \beta \epsilon_i } }{ q}\epsilon_i\].

  7. Frostbite
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[\Large \left( \frac{ \partial U_m }{ \partial T } \right)_V \approx 1.95 \sf \frac{ J}{ mol \times K }\]

  8. Frostbite
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    And my handwritten notes (the reason I don't study math)

  9. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.