By Oosthuizen P.H., Naylor D.
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Extra resources for Introduction to Convective Heat Transfer Analysis
Example text
The values taken on by S range from 2 to 12. 21) eq. 22) Do the sum over y first. Its value depends on whether s = x + y for some value of y, or equivalently, whether s − x is in the interval [1, 6]. 23) This places two conditions on the remaining sum over x. Only those values of x for which both x ≤ s − 1 and x ≥ s − 6 contribute to the final answer. 3 Determining the limits for the second sum when evaluating eq. 22). lower limit upper limit x≥1 x≥s−6 x≤6 x≤s−1 More restrictive if s ≤ 7 x≥1 x≤s−1 More restrictive if s ≥ 7 x≥s−6 x≤6 Limits on sum: From the Kronecker delta: in addition to the limits of x ≤ 6 and x ≥ 1 that are already explicit in the sum on X.
Pμ (n) = 1 n μ exp(−μ) n! 1. Modify (a copy of) your program to read in the values of μ and N and calculate the value of the probability p. Include an extra column in your output that gives the theoretical probability based on the Poisson distribution. (Note: It might be quite important to suppress rows in which the histogram is zero. ) 2. Run your program for various values of μ and N . How large does N have to be for the agreement to be good? 4 The Classical Ideal Gas: Configurational Entropy S = k log W Inscription on Boltzmann’s tombstone (first written in this form by Max Planck in 1900) This chapter begins the derivation of the entropy of the classical ideal gas, as outlined in Chapter 2.
Q = {ri |i = 1, . . 1) = {xi , yi , zi |i = 1, . . , N } = {qj |j = 1, . . , 3N } The momentum of every particle can be represented as a point in momentum space—an abstract 3N -dimensional space, with axes for every component of the momentum of every particle. p = {pi |i = 1, . . 2) = {px,i , py,i , py,i |i = 1, . . , N } = {pj |j = 1, . . , 3N } The complete microscopic state of the system can be described by a point in phase space—an abstract 6N -dimensional space with axes for every coordinate and every momentum component for all N particles.