p847ps1 - N is given by eq(20 or eq(21 oF Pathria Sec(6.3...

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Physics 847: Problem Set 1 Due Thursday, April 8 at 11:59 P. M. Each problem is worth 10 pts. unless otherwise specifed. 1. Pathria, Problem (5.6). “N. T. P.” means “Normal Temperature and Pressure,” i. e., T = 300 K, P = 1 atmosphere. 2. Pathria, Problem (6.1). Only do the part involving Fermions, and do not prove the connection to the general Formula. 3. Pathria, Problem (6.2). Do the derivation only For Fermi and bose statistics, not “all three statistics.” Also, omit the comparison with Formula (4.5.3). 4. Consider a hypothetical gas oF either Free Fermions or Free bosons at temperature T , chemical potential μ , and volume V , as discussed in class. Also, For simplicity, assume that these particles are spinless. The total number oF particles
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Unformatted text preview: N is given by eq. (20) or eq. (21) oF Pathria, Sec. (6.3). Alternatively, For Fermions, you can use the last Formula on p. 16 oF my notes, and For bosons, youcan use an analogous Formula. Now consider the “classical limit” in which the occupation number oF any given state is much smaller than 1. In this limit, frst obtain an expression For the occupation number as a Function oF energy. Show that this expression is the same as the Maxwell-Boltzmann Formula. Also, obtain an expression For μ in terms oF N , V , and T , valid For both Fermions and bosons, in this limit. Show that this expression is the same as that obtained last quarter From treatment oF the classical ideal gas. 1...
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