Chapter 3 Interactions and Implications

Entropy

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

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

Lets prove the 0 th law of thermodynamics.

An example with the Einstein Solid

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

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

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 )

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 doesnt get that cold.

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.

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.

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?

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.

m1m1 m2m2 Stars and Black Holes modeled as orbiting particles r r 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

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.

Entropy

The Thermodynamic Identity

Paramagnet

U B B Down, antiparallel Up, parallel

Paramagnet

M and U only differ by B

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

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

Analytical Paramagnet

Paramagnet

Paramagnet Properties

Paramagnet Heat Capacity

Magnetic Energies