Feed: Dr. Myron Evans
Posted on: Monday, June 10, 2013 2:11 AM
Author: metric345
Subject: Graphing Note 245(5)
Many thanks, yes the original x has a minus sign, and these graphs are full of interest. My next step is to consider the well known Debye correction of the Einstein theory, and to develop the Debye theory with R theory. In this way R theory can be applied to thermodynamics and black body radiation.
To: EMyrone@aol.com
Sent: 10/06/2013 08:06:29 GMT Daylight Time
Subj: Re: Final Version of Note 243(5)
I think x reads correctly (with a minus sign in the exponent):
x = exp( – hbar omega / (k T)).
Attached is the computer output. Eq. 17 can even be solved analytically, but the special logarithmic function li[n] is not defined in Maxima for n>3. Therefore I did a numerical integration which is quite stable. The integrand dU^2/domega is shown in the first plot and is of well known form. the integral is dependent on T and is shown in the second graph as a function of T. Because the area below the integrand increases wit T, U^2 raises accordingly. The square root of this, U, is larger than U^2 because the numerical values are below 1.
Horst
243(5).pdf
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