- #1
Jolb
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I'm working through Kardar's Statistical Physics of Particles, and I'm in chapter 4 on the part about the ideal gas. Here's a link to that chapter from the book:
http://web.mit.edu/8.333/www/lectures/lec13.pdf
I think he has an error in equation IV.33 but I'd like you guys to make sure of it.
http://img694.imageshack.us/img694/467/kardar.jpg
I think in the top equation of IV.33, the 2∏mE should be 4∏mE, so the final equation should have an 8 instead of a 4. Here's why I think that:
[tex]ln\left (V^N\frac{2\pi^\frac{3N}{2}}{\left (\frac{3N}{2}-1 \right )!} \left ( 2mE \right )^\frac{3N-1}{2}\Delta _R\right ) [/tex]
[tex]=Nln(V)+\frac{3N}{2}ln(2\pi)-\left (\frac{3N}{2}-1 \right )ln\left ( \frac{3N}{2}-1 \right )+\left ( \frac{3N}{2}-1 \right )+\frac{3N-1}{2}ln(2mE)+ln\Delta _R[/tex]
eliminating terms of order 1 or lnN,
[tex]=Nln(V)+\frac{3N}{2}ln(2\pi)-\left (\frac{3N}{2} \right )ln\left ( \frac{3N}{2} \right )+\left ( \frac{3N}{2} \right )+\frac{3N}{2}ln(2mE)[/tex]
[tex]=N\left (ln(V)+\frac{3}{2}ln(2\pi)-\left (\frac{3}{2} \right )ln\left ( \frac{3N}{2} \right )+\left ( \frac{3}{2} \right )ln(e)+\frac{3}{2}ln(2mE) \right )[/tex]
[tex]=N\left (ln(V)+ln(2\pi)^\frac{3}{2}-ln\left ( \frac{3N}{2} \right )^\frac{3}{2}+ln(e)^\frac{3}{2}+ln(2mE)^\frac{3}{2} \right )[/tex]
[tex]=Nln\left (V\left [\frac{(2\pi)(e)(2mE)}{\frac{3N}{2}} \right ]^\frac{3}{2} \right )[/tex]
Did I make a mistake eliminating the terms of lower order? Please help!
http://web.mit.edu/8.333/www/lectures/lec13.pdf
I think he has an error in equation IV.33 but I'd like you guys to make sure of it.
http://img694.imageshack.us/img694/467/kardar.jpg
I think in the top equation of IV.33, the 2∏mE should be 4∏mE, so the final equation should have an 8 instead of a 4. Here's why I think that:
[tex]ln\left (V^N\frac{2\pi^\frac{3N}{2}}{\left (\frac{3N}{2}-1 \right )!} \left ( 2mE \right )^\frac{3N-1}{2}\Delta _R\right ) [/tex]
[tex]=Nln(V)+\frac{3N}{2}ln(2\pi)-\left (\frac{3N}{2}-1 \right )ln\left ( \frac{3N}{2}-1 \right )+\left ( \frac{3N}{2}-1 \right )+\frac{3N-1}{2}ln(2mE)+ln\Delta _R[/tex]
eliminating terms of order 1 or lnN,
[tex]=Nln(V)+\frac{3N}{2}ln(2\pi)-\left (\frac{3N}{2} \right )ln\left ( \frac{3N}{2} \right )+\left ( \frac{3N}{2} \right )+\frac{3N}{2}ln(2mE)[/tex]
[tex]=N\left (ln(V)+\frac{3}{2}ln(2\pi)-\left (\frac{3}{2} \right )ln\left ( \frac{3N}{2} \right )+\left ( \frac{3}{2} \right )ln(e)+\frac{3}{2}ln(2mE) \right )[/tex]
[tex]=N\left (ln(V)+ln(2\pi)^\frac{3}{2}-ln\left ( \frac{3N}{2} \right )^\frac{3}{2}+ln(e)^\frac{3}{2}+ln(2mE)^\frac{3}{2} \right )[/tex]
[tex]=Nln\left (V\left [\frac{(2\pi)(e)(2mE)}{\frac{3N}{2}} \right ]^\frac{3}{2} \right )[/tex]
Did I make a mistake eliminating the terms of lower order? Please help!
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