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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


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    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.
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