An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Question
Chapter 2.4, Problem 22P
(a)
To determine
To Find: The different microstates for the system of two identical Einstein solids.
(b)
To determine
To Find: In combined system find the approximate expression for total number of microstates.
(c)
To determine
To Find: In combined system find the approximate expression for the multiplicity of microstates.
(d)
To determine
To Find: The fraction of microstates having large probabilities.
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Students have asked these similar questions
a) Make a diagram showing how many distinct ways (how many microstates, the
multiplicity) there are of putting q = 2 indistinguishable objects in N = 3 boxes.
Assuming that all microstates are equally probable, what is the probability that
both objects are in the left-most box? What is the correct formula for the
mulitiplicity as a function of N and q?
b) Make a diagram showing how many distinct ways (the multiplicity) there are of
putting q = 2 distinguishable objects in N= 3 boxes. Assuming that all microstates
are equally probable, what is the probability that both objects are in the left-most
box? Label the two objects R and G. What is the correct formula for the
mulitiplicity as a function of N and q?
Below are the diagrams, started for you. Complete the diagrams.
distinguishable
indistinguishable
RG
•.
!R !G
Consider N identical harmonic oscillators (as in the Einstein floor). Permissible Energies of each oscillator (E = n h f (n = 0, 1, 2 ...)) 0, hf, 2hf and so on.
A) Calculating the selection function of a single harmonic oscillator. What is the division of N oscillators?
B) Obtain the average energy of N oscillators at temperature T from the partition function.
C) Calculate this capacity and T-> 0 and At T-> infinity limits, what will the heat capacity be? Are these results consistent with the experiment? Why? What is the correct theory about this?
D) Find the Helmholtz free energy from this system.
E) Derive the expression that gives the entropy of this system for the temperature.
The Einstein model for a solid assumes the system consists of 3N independent simple harmonic oscillators with frequencies &. Within these assumptions, the heat capacity at constant volume as:
Cv=3Nk() (-1)²
²
Complete the table for the molar heat capacity at various temperatures under either the Einstein model or high-temperature limit. You might like to use the Wolfram Alpha calculator to do the numerical calculations more
easily. Use k-0.695 cm /K.
High temperature limit value of molar heat capacity of metal is
T
1 K
10 K
50 K
-1
Einstein, = 100 cm Einstein, : = 500 cm
1.4021
3.8991
100 K
500 K
2.434E-4
1000 K
6.1499
2434E-4
kJ/mol.
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...
Knowledge Booster
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