An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter 2.4, Problem 18P
To determine
To Explain:The multiplicity of an Einstein solid for any values of N and q is
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Calculate Z for a single oscillator in an Einstein solid at a temperature T=4TE=4ϵ/kBT=4 TE=4 ϵ/kB .
The value of Z is
Suppose an Einstein Solid is in equilibrium with a reservoir at some temperature T. Assume the ground
state energy is 0, the solid is composed of N oscillators, and the size of an energy "unit" is e.
(a) Find the partition function for a single oscillator in the solid, Z1.
Hint: use the general series summation formula 1+ x + x? + x³ + ... = 1/ (1- x)
(b) Find an expression for , the average energy per oscillator in the solid, in terms of kT and e.
(c) Find the total energy of the solid as a function of T, using the expression from part (b).
(d) Suppose e = 2 eV and T = 25°C. What fraction of the oscillators is in the first excited state, compared
to the ground state (assuming no degeneracies of energy levels)?
Calculate Z for a single oscillator in an Einstein solid at a temperature T = 2TE = 2Ɛ/kB.
Chapter 2 Solutions
An Introduction to Thermal Physics
Ch. 2.1 - Prob. 1PCh. 2.1 - Prob. 2PCh. 2.1 - Prob. 3PCh. 2.1 - Prob. 4PCh. 2.2 - For an Einstein solid with each of the following...Ch. 2.2 - Prob. 6PCh. 2.2 - Prob. 7PCh. 2.3 - Prob. 8PCh. 2.3 - Use a computer to reproduce the table and graph in...Ch. 2.3 - Use a computer to produce a table and graph, like...
Ch. 2.3 - Use a computer to produce a table and graph, like...Ch. 2.4 - Prob. 12PCh. 2.4 - Fun with logarithms. (a) Simplify the expression...Ch. 2.4 - Write e1023 in the form 10x, for some x.Ch. 2.4 - Prob. 15PCh. 2.4 - Prob. 16PCh. 2.4 - Prob. 17PCh. 2.4 - Prob. 18PCh. 2.4 - Prob. 19PCh. 2.4 - Suppose you were to shrink Figure 2.7 until the...Ch. 2.4 - Prob. 21PCh. 2.4 - Prob. 22PCh. 2.4 - Prob. 23PCh. 2.4 - Prob. 24PCh. 2.4 - Prob. 25PCh. 2.5 - Prob. 26PCh. 2.5 - Prob. 27PCh. 2.6 - How many possible arrangements are there for a...Ch. 2.6 - Consider a system of two Einstein solids, with...Ch. 2.6 - Prob. 30PCh. 2.6 - Fill in the algebraic steps to derive the...Ch. 2.6 - Prob. 32PCh. 2.6 - Use the Sackur-Tetrode equation to calculate the...Ch. 2.6 - Prob. 34PCh. 2.6 - According to the Sackur-Tetrode equation, the...Ch. 2.6 - For either a monatomic ideal gas or a...Ch. 2.6 - Using the Same method as in the text, calculate...Ch. 2.6 - Prob. 38PCh. 2.6 - Compute the entropy of a mole of helium at room...Ch. 2.6 - For each of the following irreversible process,...Ch. 2.6 - Describe a few of your favorite, and least...Ch. 2.6 - A black hole is a region of space where gravity is...
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