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Chapter 3 Interactions and Implications

Chapter 3 Interactions and Implications. Entropy

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Page 1: Chapter 3 Interactions and Implications. Entropy

Chapter 3

Interactions and Implications

Page 2: Chapter 3 Interactions and Implications. Entropy

Entropy

Page 3: Chapter 3 Interactions and Implications. Entropy

Entropy

Page 4: Chapter 3 Interactions and Implications. Entropy

Let’s show that the derivative of entropy with respect to energy is temperature for the Einstein solid.

Page 5: Chapter 3 Interactions and Implications. Entropy

Let’s show that the derivative of entropy with respect to energy is temperature for the monatomic ideal gas.

Page 6: Chapter 3 Interactions and Implications. Entropy

Let’s prove the 0th law of thermodynamics.

Page 7: Chapter 3 Interactions and Implications. Entropy

An example with the Einstein Solid

Page 8: Chapter 3 Interactions and Implications. Entropy

Easy – we’ll see a better way in Ch . 6 w/o needing W

Heat Capacity, Entropy, Third Law• Calculate W

• Calculate S = k B ln(W)

• Calculate dS/dU = 1/T

• Solve for U(T)

• C v = dU/dT

Difficult to impossible

Easy

Easy

Easy

Page 9: Chapter 3 Interactions and Implications. Entropy

Heat capacity of aluminum

Let’s calculate the entropy changes in our heat capacity experiment.

Page 10: Chapter 3 Interactions and Implications. Entropy

Heat Capacity, Entropy, Third Law

What were the entropy changes in the water and aluminum?

DS = Sf – Si = C ln(Tf/Ti)

Page 11: Chapter 3 Interactions and Implications. Entropy

Heat Capacity, Entropy, Third Law

As a system approaches absolute zero temperature, all processes within the system cease, and the entropy approaches a minimum.

Page 12: Chapter 3 Interactions and Implications. Entropy

The Third Law

As a system approaches absolute zero temperature, all processes within the system cease, and the entropy approaches a minimum.

It doesn’t get that cold.

limT 0

S 0

limT 0

CV 0

Page 13: Chapter 3 Interactions and Implications. Entropy

m1

m2

Stars and Black Holes modeled as orbiting particles

rr

Show the potential energy is equal to negative 2 times the kinetic energy.

Page 14: Chapter 3 Interactions and Implications. Entropy

m1

m2

Stars and Black Holes modeled as orbiting particles

rr

Show the potential energy is equal to negative 2 times the kinetic energy.

Page 15: Chapter 3 Interactions and Implications. Entropy

m1

m2

Stars and Black Holes modeled as orbiting particles

rr

What happens when energy is added? If modeled as an ideal gas what is the total energy and heat capacity in terms of T?

Page 16: Chapter 3 Interactions and Implications. Entropy

m1

m2

Stars and Black Holes modeled as orbiting particles

rr

Use dimensional analysis to argue potential energy should be of order -GM2/R. Estimate the number of particles and temperature of our sun.

Page 17: Chapter 3 Interactions and Implications. Entropy

m1

m2

Stars and Black Holes modeled as orbiting particles

rr

What is the entropy of our sun?

Page 18: Chapter 3 Interactions and Implications. Entropy

Black Holes

What is the entropy a solar mass black hole?

Page 19: Chapter 3 Interactions and Implications. Entropy

Black Holes

What are the entropy and temperature a solar mass black hole?

Page 20: Chapter 3 Interactions and Implications. Entropy

S

U

Page 21: Chapter 3 Interactions and Implications. Entropy

Mechanical Equilibrium

Page 22: Chapter 3 Interactions and Implications. Entropy

Mechanical Equilibrium

Page 23: Chapter 3 Interactions and Implications. Entropy

Mechanical Equilibrium

Page 24: Chapter 3 Interactions and Implications. Entropy

Diffusive Equilibrium

Page 25: Chapter 3 Interactions and Implications. Entropy

Diffusive Equilibrium

Chemical potential describes how particles move.

Page 26: Chapter 3 Interactions and Implications. Entropy

The Thermodynamic Identity

Page 27: Chapter 3 Interactions and Implications. Entropy

Diffusive Equilibrium

Chemical potential describes how particles move.

Page 28: Chapter 3 Interactions and Implications. Entropy

Diffusive Equilibrium

Chemical potential describes how particles move.

Page 29: Chapter 3 Interactions and Implications. Entropy

Diffusive Equilibrium

Chemical potential describes how particles move.

Page 30: Chapter 3 Interactions and Implications. Entropy

Diffusive Equilibrium

Chemical potential describes how particles move.

Page 31: Chapter 3 Interactions and Implications. Entropy

Entropy

http://www.youtube.com/watch?v=dBXL93984cQ

Page 32: Chapter 3 Interactions and Implications. Entropy

The Thermodynamic Identity

Page 33: Chapter 3 Interactions and Implications. Entropy

The Thermodynamic Identity

Page 34: Chapter 3 Interactions and Implications. Entropy

Paramagnet

Page 35: Chapter 3 Interactions and Implications. Entropy

Paramagnet

U

+mB

-mB

0

Down, antiparallel

Up, parallel

Page 36: Chapter 3 Interactions and Implications. Entropy

Paramagnet

Page 37: Chapter 3 Interactions and Implications. Entropy

Paramagnet

Page 38: Chapter 3 Interactions and Implications. Entropy

Paramagnet• M and U only differ by B

Page 39: Chapter 3 Interactions and Implications. Entropy

Nuclear Magnetic Resonance

wo = 900 MHzB = 21.2 Two = g Bg = 42.4 (for protons)

Page 40: Chapter 3 Interactions and Implications. Entropy

Nuclear Magnetic Resonance

Inversion recoveryQuickly reverse magnetic fieldB

NmB

BNmB

U

S

Low U (negative stable)Work on system lowers entropybut it will absorb any availableenergy to try and slide towards max S

High U (positive unstable)Work on system lowers entropybut it will absorb any availableenergy to try and slide towards max S

M NmB

t

Page 41: Chapter 3 Interactions and Implications. Entropy

Analytical Paramagnet

Page 42: Chapter 3 Interactions and Implications. Entropy

Analytical Paramagnet

Page 43: Chapter 3 Interactions and Implications. Entropy

Analytical Paramagnet

Page 44: Chapter 3 Interactions and Implications. Entropy

Analytical Paramagnet

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Paramagnet

Page 46: Chapter 3 Interactions and Implications. Entropy

Paramagnet Properties

Page 47: Chapter 3 Interactions and Implications. Entropy

Paramagnet Properties

Page 48: Chapter 3 Interactions and Implications. Entropy

Paramagnet Heat Capacity

Page 49: Chapter 3 Interactions and Implications. Entropy

Magnetic Energies