An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Question
Chapter 3.5, Problem 36P
(a)
To determine
To Show:The chemical potential of Einstein solid is
(b)
To determine
The results in the limits
The chemical potential when a particle with no energy is added to the system.
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Problem 3: Chemical potential of an Einstein solid.
Consider an Einstein solid for which both N and q are much greater than 1. Think of each
ocillator as a separate “particle".
a) Show that the chemical potential is
H = -kT In (**e)
b) Discuss this result in the limits N » q and N « q, concentrating on the question of how
much S increases when another particle carrying no energy is added to the system. Does
the formula make intuitive sense?
Consider a system of two Einstein solids, where the first "solid" contains just a single oscillator, while the second solid contains 100 oscillators. The total number of energy units in the combined system is fixed at 500. Use a computer to make a table of the multiplicity of the combined system, for each possible value of the energy of the first solid from 0 units to 20. Make a graph of the total multiplicity vs. the energy of the first solid, and discuss, in some detail, whether the shape of the graph is what you would expect. Also plot the logarithm of the total multiplicity, and discuss the shape of this graph.
A triangle in the xy plane is defined with
corners at (x, y) = (0,0), (0, 2) and
(4, 2). We want to integrate some
function f(x, y) over the interior of this
triangle.
Choosing dx as the inner integral, the
required expression to integrate is given
by:
Select one:
o Sro S-o f(x, y) dx dy
x=0
2y
y=0
O S-o So F(x, y) dæ dy
O o S f(x, y) dy dæ
O So So F(x, y) dx dy
x/2
=0
Chapter 3 Solutions
An Introduction to Thermal Physics
Ch. 3.1 - Use Table 3.1 to compute the temperature of solid...Ch. 3.1 - Use the definition of temperature to prove the...Ch. 3.1 - Figure 3.3 shows graphs of entropy vs. energy for...Ch. 3.1 - Can a miserly system, with a concave-up...Ch. 3.1 - Prob. 5PCh. 3.1 - Prob. 6PCh. 3.1 - Prob. 7PCh. 3.2 - Prob. 8PCh. 3.2 - In solid carbon monoxide, each CO molecule has two...Ch. 3.2 - An ice cube (mass 30 g) at 0C is left sitting on...
Ch. 3.2 - In order to take a nice warm bath, you mix 50...Ch. 3.2 - Estimate the change in the entropy of the universe...Ch. 3.2 - When the sun is high in the sky, it delivers...Ch. 3.2 - Experimental measurements of the heat capacity of...Ch. 3.2 - Prob. 15PCh. 3.2 - A bit of computer memory is some physical object...Ch. 3.3 - Prob. 17PCh. 3.3 - Prob. 18PCh. 3.3 - Prob. 19PCh. 3.3 - Prob. 20PCh. 3.3 - Prob. 21PCh. 3.3 - Prob. 22PCh. 3.3 - Prob. 23PCh. 3.3 - Prob. 24PCh. 3.3 - Prob. 25PCh. 3.3 - Prob. 26PCh. 3.4 - What partial-derivative relation can you derive...Ch. 3.4 - A liter of air, initially at room temperature and...Ch. 3.4 - Sketch a qualitatively accurate graph of the...Ch. 3.4 - As shown in Figure 1.14, the heat capacity of...Ch. 3.4 - Experimental measurements of heat capacities are...Ch. 3.4 - A cylinder contains one liter of air at room...Ch. 3.4 - Prob. 33PCh. 3.4 - Polymers, like rubber, are made of very long...Ch. 3.5 - Prob. 35PCh. 3.5 - Prob. 36PCh. 3.5 - Prob. 37PCh. 3.5 - Suppose you have a mixture of gases (such as air,...Ch. 3.6 - Prob. 39P
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