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Chapter 3 Interactions and Implications

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Entropy

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

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

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Lets prove the 0 th law of thermodynamics.

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An example with the Einstein Solid

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Easy – well see a better way in Ch. 6 w/o needing Heat Capacity, Entropy, Third Law Calculate Calculate S = k B ln( ) Calculate dS/dU = 1/T Solve for U(T) C v = dU/dT Difficult to impossible Easy

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Heat capacity of aluminum Lets calculate the entropy changes in our heat capacity experiment.

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Heat Capacity, Entropy, Third Law What were the entropy changes in the water and aluminum? S = S f – S i = C ln(T f /T i )

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Heat Capacity, Entropy, Third Law As a system approaches absolute zero temperature, all processes within the system cease, and the entropy approaches a minimum.

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The Third Law As a system approaches absolute zero temperature, all processes within the system cease, and the entropy approaches a minimum. It doesnt get that cold.

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m1m1 m2m2 Stars and Black Holes modeled as orbiting particles r r Show the potential energy is equal to negative 2 times the kinetic energy.

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m1m1 m2m2 Stars and Black Holes modeled as orbiting particles r r Show the potential energy is equal to negative 2 times the kinetic energy.

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m1m1 m2m2 Stars and Black Holes modeled as orbiting particles r r What happens when energy is added? If modeled as an ideal gas what is the total energy and heat capacity in terms of T?

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m1m1 m2m2 Stars and Black Holes modeled as orbiting particles r r Use dimensional analysis to argue potential energy should be of order -GM 2 /R. Estimate the number of particles and temperature of our sun.

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m1m1 m2m2 Stars and Black Holes modeled as orbiting particles r r What is the entropy of our sun?

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Black Holes What is the entropy a solar mass black hole?

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

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S U

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Mechanical Equilibrium

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Diffusive Equilibrium

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Chemical potential describes how particles move.

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The Thermodynamic Identity

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Diffusive Equilibrium Chemical potential describes how particles move.

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Diffusive Equilibrium Chemical potential describes how particles move.

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Diffusive Equilibrium Chemical potential describes how particles move.

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Diffusive Equilibrium Chemical potential describes how particles move.

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Entropy

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The Thermodynamic Identity

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Paramagnet

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U B B Down, antiparallel Up, parallel

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Paramagnet

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M and U only differ by B

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Nuclear Magnetic Resonance = 900 MHz B = 21.2 T = B = 42.4 (for protons)

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Nuclear Magnetic Resonance Inversion recovery Quickly reverse magnetic field B N B B U S Low U (negative stable) Work on system lowers entropy but it will absorb any available energy to try and slide towards max S High U (positive unstable) Work on system lowers entropy but it will absorb any available energy to try and slide towards max S M N B t

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Analytical Paramagnet

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Paramagnet

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Paramagnet Properties

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Paramagnet Heat Capacity

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Magnetic Energies

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