1. Not finding help here? Sign up for a free 30min 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!

Heat Capacity of a classical ideal gas and SHO

  1. Jan 27, 2013 #1
    1. The problem statement, all variables and given/known data
    Ideal gas. In an ideal-gas model. N molecules move almost indepdently with very weak interactions between, in a three-dimensional box of volume V. Find the heat capacity of the system.

    SHO. Consider N independent SHOs in a system. each osciallating about a fixed point. The spring constant is assumed to be k and the mass of oscillator m. FInd the heat capacity.


    2. Relevant equations
    I understand heat capacity can be described as change of energy (E) over time (T) so:

    Cv (heat capacity) = (dE/dT * dS/dE)*T
    = dS/dT*T


    3. The attempt at a solution

    I have S, but I am having trouble with taking the derivative of dS/dT. do i bring the T over so i can take dS/dT?

    The S that I have is:

    S = N*Kb*ln((V/h^3)*(((4*pi*m*E)/(3N)))*^(3/2)+3/2N

    having trouble going from here since if it is S/T, my heat capacity would just be -S/T^2??

    Thanks in advance for the help
     
  2. jcsd
  3. Jan 27, 2013 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Temperature, not time. And your equation relates entropy changes to temperature, not energy changes.

    With your S, you can calculate dS/dE. But that is just the inverse temperature:
    $$\frac{1}{T}=\frac{\partial S}{\partial E}$$
    With an expression E(T), you can calculate the heat capacity.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Heat Capacity of a classical ideal gas and SHO
  1. Heating an ideal gas (Replies: 2)

Loading...