Using Sackur-Tetrode Formula to Verify Average Kinetic Energy of an Ideal Gas

[kasse]

Homework Statement

Use the Sackur-Tetrode formula to verify that the average kinetic energy of an ideall gas is \frac{3}{2}k_B T.

Homework Equations

Sackur-Tetrode:

<br /> S_{tot}(E_A) = k_B[N_A(\frac{3}{2}ln \ E_A + ln \ V_A) + N_B(\frac{3}{2}ln(E_{tot} - E_A) + ln \ V_B)] + const.<br />

The Attempt at a Solution

The average value is the most probable value, because of gaussian distribution. Derivation gives:

<br /> 0 \ = \ \frac{dS_{tot}}{dE_A} \ = \ \frac{3}{2}k_B(\frac{N_A}{E_A} - \frac{N_B}{E_B})<br />

Am I on the right track? What can I do next? Simply set
E_A = E_B = \frac{3}{2}k_BT
and
N_A = N_B?

 

[tinytoon]

this is probably too late a response for you, but I'll post it for future readers:

The Sackur-Tetrode equation is:
<br /> S = Nk (ln \left(\frac{4V^{2/3} \pi mU}{3N^{5/3}h^2}\right) +5/2)<br />
Just take the derivative with respect to U:
<br /> \frac{\partial S}{\partial U} = \frac{1}{T} = \frac{3Nk}{2U}<br />
Rearrange and it gives:
<br /> U = \frac{3}{2} NkT<br />