Slide 1

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Problem 6.6 K&K:
Entropy of mixing. Suppose that a system of N atoms
of type A is placed in diffusive contact with a system of
N atoms of type B at the same temperature and volume.
Show that after diffusive equilibrium is reached the total
entropy is increased by 2Nlog2. The entropy increase
2Nlog2 is known as the entropy of mixing. If the atoms
are identical (A=B), show that there is no increase in
entropy when diffusive contact is established. The
difference in the results has been called the Gibbs paradox.
Hand in: your scratch paper showing your thought process and
work, as well as interpretation of your result.


Slide 2

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Problem 6.6 K&K:
Entropy of mixing. Suppose that a system of N atoms
of type A is placed in diffusive contact with a system of
N atoms of type B at the same temperature and volume.
Show that after diffusive equilibrium is reached the total
entropy is increased by 2Nlog2. The entropy increase
2Nlog2 is known as the entropy of mixing. If the atoms
are identical (A=B), show that there is no increase in
entropy when diffusive contact is established. The
difference in the results has been called the Gibbs paradox.
Hand in: your scratch paper showing your thought process and
work, as well as interpretation of your result.


Slide 3

0

Problem 6.6 K&K:
Entropy of mixing. Suppose that a system of N atoms
of type A is placed in diffusive contact with a system of
N atoms of type B at the same temperature and volume.
Show that after diffusive equilibrium is reached the total
entropy is increased by 2Nlog2. The entropy increase
2Nlog2 is known as the entropy of mixing. If the atoms
are identical (A=B), show that there is no increase in
entropy when diffusive contact is established. The
difference in the results has been called the Gibbs paradox.
Hand in: your scratch paper showing your thought process and
work, as well as interpretation of your result.


Slide 4

0

Problem 6.6 K&K:
Entropy of mixing. Suppose that a system of N atoms
of type A is placed in diffusive contact with a system of
N atoms of type B at the same temperature and volume.
Show that after diffusive equilibrium is reached the total
entropy is increased by 2Nlog2. The entropy increase
2Nlog2 is known as the entropy of mixing. If the atoms
are identical (A=B), show that there is no increase in
entropy when diffusive contact is established. The
difference in the results has been called the Gibbs paradox.
Hand in: your scratch paper showing your thought process and
work, as well as interpretation of your result.


Slide 5

0

Problem 6.6 K&K:
Entropy of mixing. Suppose that a system of N atoms
of type A is placed in diffusive contact with a system of
N atoms of type B at the same temperature and volume.
Show that after diffusive equilibrium is reached the total
entropy is increased by 2Nlog2. The entropy increase
2Nlog2 is known as the entropy of mixing. If the atoms
are identical (A=B), show that there is no increase in
entropy when diffusive contact is established. The
difference in the results has been called the Gibbs paradox.
Hand in: your scratch paper showing your thought process and
work, as well as interpretation of your result.


Slide 6

0

Problem 6.6 K&K:
Entropy of mixing. Suppose that a system of N atoms
of type A is placed in diffusive contact with a system of
N atoms of type B at the same temperature and volume.
Show that after diffusive equilibrium is reached the total
entropy is increased by 2Nlog2. The entropy increase
2Nlog2 is known as the entropy of mixing. If the atoms
are identical (A=B), show that there is no increase in
entropy when diffusive contact is established. The
difference in the results has been called the Gibbs paradox.
Hand in: your scratch paper showing your thought process and
work, as well as interpretation of your result.


Slide 7

0

Problem 6.6 K&K:
Entropy of mixing. Suppose that a system of N atoms
of type A is placed in diffusive contact with a system of
N atoms of type B at the same temperature and volume.
Show that after diffusive equilibrium is reached the total
entropy is increased by 2Nlog2. The entropy increase
2Nlog2 is known as the entropy of mixing. If the atoms
are identical (A=B), show that there is no increase in
entropy when diffusive contact is established. The
difference in the results has been called the Gibbs paradox.
Hand in: your scratch paper showing your thought process and
work, as well as interpretation of your result.


Slide 8

0

Problem 6.6 K&K:
Entropy of mixing. Suppose that a system of N atoms
of type A is placed in diffusive contact with a system of
N atoms of type B at the same temperature and volume.
Show that after diffusive equilibrium is reached the total
entropy is increased by 2Nlog2. The entropy increase
2Nlog2 is known as the entropy of mixing. If the atoms
are identical (A=B), show that there is no increase in
entropy when diffusive contact is established. The
difference in the results has been called the Gibbs paradox.
Hand in: your scratch paper showing your thought process and
work, as well as interpretation of your result.


Slide 9

0

Problem 6.6 K&K:
Entropy of mixing. Suppose that a system of N atoms
of type A is placed in diffusive contact with a system of
N atoms of type B at the same temperature and volume.
Show that after diffusive equilibrium is reached the total
entropy is increased by 2Nlog2. The entropy increase
2Nlog2 is known as the entropy of mixing. If the atoms
are identical (A=B), show that there is no increase in
entropy when diffusive contact is established. The
difference in the results has been called the Gibbs paradox.
Hand in: your scratch paper showing your thought process and
work, as well as interpretation of your result.