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!

Thermodynamics - (polymer) caluclate the average potential energy

  1. Dec 21, 2013 #1
    1. The problem statement, all variables and given/known data
    A polymer of ##10^{20}## molecules each 2nm long is hanged from the ceiling. The other end of the polymer is attached to a ##m=4\cdot 10^{-10} g## load. Calculate the average potential energy! Temperature is 300 K.

    2. Relevant equations
    ##<E>=<E_p>=\frac{\mathrm{d} (\beta F)}{\mathrm{d} \beta }##

    ##e^{-\beta F}=\sum_{n}^{N}c_ne^{-\beta E_n}##

    3. The attempt at a solution

    if ##e^{-\beta F}=\sum_{n}^{N}c_ne^{-\beta E_n}## than

    ##e^{-\beta F}=\sum_{n=0}^{N=10^{20}}c_ne^{-\beta E_n}##

    Now, I'm not sure, but I think that ##E_n## which is potential energy of one particular molecule should be ##E_n=mgln## if l is lenght of one molecule.

    therefore ##e^{-\beta F}=\sum_{n=0}^{N=10^{20}}c_ne^{-\beta mgln}##

    This is now ##e^{-\beta F}=\frac{e^{-\beta mgl(N+1)}-1}{e^{-\beta mgl}-1}##

    so ##\beta F=ln(e^{-\beta mgl}-1)-ln(e^{-\beta mgl(N+1)}-1)##

    and

    ##<E>=<E_p>=\frac{\mathrm{d} (\beta F)}{\mathrm{d} \beta }=mgl(\frac{(N+1)e^{-\beta mgl(N+1)}}{e^{-\beta mgl(N+1)}-1}-\frac{1}{e^{-\beta mgl}-1})##

    BUT this gives me ##E_p=9.23\cdot 10^{-21}J## which is only 2.35 nanometers... I siriously doubt that is the case :/ Does anybody know what's wrong here?

    Thanks for all the help!
     
    Last edited: Dec 21, 2013
  2. jcsd
  3. Dec 21, 2013 #2
    okej everything above is completely wrong.

    I think it goes something like this: ##e^{-\beta F}=\sum_{n=0}^{N}e^{-\beta E_n}##

    where ##E_n=-mgh(n)## but the key here is to write h as function of n... Now that's all i have..
     
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: Thermodynamics - (polymer) caluclate the average potential energy
Loading...