Ø Course web address: rossgroup.tamu.edu/408page.html Syllabus will be posted there, same as our printed syllabus. (Bibliography, course slides & notes, etc. also as we go along.)

Ø Grading: 1 midterm + 1 final, also Homework.Homework presentations: about 3 each week, everyone does one! • Work out one of the problems on the whiteboard for the class. >> Volunteer to go first if you would like.

Ø Reading: Ch. 1-2 this week. Ø Final note regarding slides: You should take notes also; I

don’t put everything on slides.

Phys 408: Thermodynamics /Statistical Mechanics

Thermodynamics : macroscopic thermal physics

Statistical mechanics : microscopic, ”atoms up”

properties.

>> Here we deal with with collections or “ensembles” of particles

or objects.

Thermodynamics : macroscopic thermal physics

Statistical mechanics : microscopic, ”atoms up”

properties, but applied in statistical way.

>> Here we deal with with collections or “ensembles” of particles

or objects.

Entropy (S), dS = !"# , heat flow vs. temperature: Clausius, Carnot mid 1800’s.

Boltzmann: S = kB ln Ω; Ω = countable number of statesto be explored by particles in system.

Some applications:

• Fermi & Bose gases: quantum behavior underlies everyday

behavior of metals, nuclei & nuclear matter, neutron stars.

• Quantum information theory, connection to black hole entropy,

Hawking radiation etc.

• “Quantum thermodynamics”; entanglement vs.

random/statistical behavior of interacting systems.

Processes and Variables:

Q = Heat; Spontaneous energy flow into system, not by changing external variables.

E = Total internal energy. • Potential + Kinetic energy summed over all parts of system.

W = Work done on system; energy transfer to system via changing external variable.

most obvious example: compression, e.g. by piston (W = – P dV.)work also includes all energy transfer processes other than heat flow.

Refer to specific processes (change along a specific path) Reversible or irreversible.

Processes

State function

Processes and Variables:

Q = Heat; Spontaneous energy flow into system, not by changing external variables.

E = Total internal energy. S (Entropy); Free energies …

W = Work done on system; energy transfer to system via changing external variable. W = – P dV controlled process

State functions:

State variables:

T, P, V, n, H, M, … Measurable properties of a systemGenerally appear as pairs (Intensive, Extensive)

Defined at equilibrium.

Example

Perfectly Insulated cylinder (Adiabatic Process) Q = 0

Expand very fast to 2x volume.sign of Q, W? ∆E? Δ"?

(N remains same inside)

(Non) Idealgas

Example

Perfectly Insulated cylinder (Adiabatic Process) Q = 0

Expand very fast to 2x volume.sign of Q, W? ∆E? Δ"?

(N remains same inside)

(Non) Idealgas

W = Work done on system; energy transfer to system via changing external variable. W = – P dV controlled process; path dependent

0 0 0 if ideal?

Perfectly Insulated cylinder (Adiabatic Process) Q = 0

Expand very fast to 2x volume.sign of Q, W? ∆E? Δ"?

(N remains same inside)

(Non) Idealgas

W = Work done on system; energy transfer to system via changing external variable. W = – P dV controlled process; path dependent

0 0 0 if ideal?

• First law (conservation of energy):

Δ# = % +'

• First law (conservation of energy):

Δ" = $ +&

W = Work done on system; e.g. Mechanical work:

−(Δ) *+ − ∫(-)Easy to derive. For controlled process only.

alternatives −./MdH; −(Δ" ; electrical work (ohmic heating)…state variables define multi-dimensional space

E = State function; ∆" ≡ "2 − "3Q, W depend on path.

Equilibrium• Macroscopic properties not changing vs. time.

• Systems in contact, reach equilibrium state:

• Flow of heat, mechanical motion etc. ceases.

• In contact for “a long time”

• Temperatures identical

• We are making assumption: interactions can

“randomize” the systems.

• Intensive properties are uniform: e.g. T, P, …

AB C

Zeroth law

Equilibrium• Macroscopic properties not changing vs. time.

• Systems in contact, reach equilibrium state:

• Flow of heat, mechanical motion etc. ceases.

• In contact for “a long time”

• Temperatures identical

• We are making assumption: interactions can

“randomize” the systems.

• Intensive properties are uniform: e.g. T, P, …

AB C

Zeroth law

• System equation of state determines external state of system based on all intensive properties.• Thermodynamics = understanding system behavior without knowing all possible microscpic parameters (each molecular speed…).

Ideal gases:

• No inter-particle interactions except r = 0 “hard-sphere”.

• Air at room T: ideal gas good approximation, but note can have

internal degrees of freedom.

• Also define quantum gases this way; classical systems also obey

PV = NkT

• Pressure vs. velocity.

from straightforward kinetics, ! = #$ % &'( ,

gas pressure in equilibrium (after time average and

sum over all states).

kB = 1.38 × 10-23 J/K = R/N

Temperature:

How to define? • Linear volume expansion dV = !VdT. Traditional thermometers.

• Defined in terms of Kinetic theory: • Translational energy (ideal, noninteracting gas) proportional to T;

• Equipartition theorem: "# $%& energy each degree of freedom

(separable variables appearing as quadratic in Hamiltonian).

• (also connects to pV = nRT as a temperature scale).

• Later macroscopic thermo definition: & = ()*)+ ,,.

S: entropy

Ideal gases:

• No inter-particle interactions.

• Can have internal degrees of freedom.

• Classical case: PV = NkT

!" =$%$& "

= $'$& "

(1st law)

!( =$%$& (

= $(' + +,)$& (

H2, N2, etc. ”ideal gases” to very good approx. at RT