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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