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Chapter 3 Interactions and Implications
Chapter 3
Interactions and Implications
Entropy
Entropy
Let’s show that the derivative of entropy with respect to energy is temperature for the Einstein solid.
Let’s show that the derivative of entropy with respect to energy is temperature for the monatomic ideal gas.
Let’s prove the 0th law of thermodynamics.
An example with the Einstein Solid
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
Heat capacity of aluminum
Let’s calculate the entropy changes in our heat capacity experiment.
Heat Capacity, Entropy, Third LawWhat were the entropy changes in the water and aluminum?
DS = Sf – Si = C ln(Tf/Ti)
Heat Capacity, Entropy, Third Law
As a system approaches absolute zero temperature, all processes within the system cease, and the entropy approaches a minimum.
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
m1
m2
Stars and Black Holes modeled as orbiting particles
rr
Show the potential energy is equal to negative 2 times the kinetic energy.
m1
m2
Stars and Black Holes modeled as orbiting particles
rr
Show the potential energy is equal to negative 2 times the kinetic energy.
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?
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.
m1
m2
Stars and Black Holes modeled as orbiting particles
rr
What is the entropy of our sun?
Black Holes
What is the entropy a solar mass black hole?
Black Holes
What are the entropy and temperature a solar mass black hole?
S
U
Mechanical Equilibrium
Mechanical Equilibrium
Mechanical Equilibrium
Diffusive Equilibrium
Diffusive Equilibrium
Chemical potential describes how particles move.
The Thermodynamic Identity
Diffusive Equilibrium
Chemical potential describes how particles move.
Diffusive Equilibrium
Chemical potential describes how particles move.
Diffusive Equilibrium
Chemical potential describes how particles move.
Diffusive Equilibrium
Chemical potential describes how particles move.
The Thermodynamic Identity
The Thermodynamic Identity
Paramagnet
Paramagnet
U
+mB
-mB
0
Down, antiparallel
Up, parallel
Paramagnet
Paramagnet
Paramagnet• M and U only differ by B
Nuclear Magnetic Resonance
wo = 900 MHzB = 21.2 Two = g Bg = 42.4 (for protons)
Nuclear Magnetic ResonanceInversion 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
Analytical Paramagnet
Analytical Paramagnet
Analytical Paramagnet
Analytical Paramagnet
Paramagnet
Paramagnet Properties
Paramagnet Properties
Paramagnet Heat Capacity
Magnetic Energies
