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For a system obeying Boltzmann statistics, we know what µ
Chapter 7, Problem 15P(choose chapter or problem)
Problem 15P
For a system obeying Boltzmann statistics, we know what µ is from Chapter 6. Suppose, though, that you knew the distribution function (equation) but didn’t know µ You could still determine µ by requiring that the total number of particles, summed over all single-particle states, equal N. Carry out this calculation, to rederive the formula µ = − kT ln( z1/N). (This is normally how µ is determined in quantum statistics, although the math is usually more difficult.)
Equation:
Questions & Answers
QUESTION:
Problem 15P
For a system obeying Boltzmann statistics, we know what µ is from Chapter 6. Suppose, though, that you knew the distribution function (equation) but didn’t know µ You could still determine µ by requiring that the total number of particles, summed over all single-particle states, equal N. Carry out this calculation, to rederive the formula µ = − kT ln( z1/N). (This is normally how µ is determined in quantum statistics, although the math is usually more difficult.)
Equation:
ANSWER:
Step 1 of 3
We know that a system of particle obeying the boltzmann distribution, the total number of particle should be
