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The 20 things to learn and
understand about
thermodynamics and condensed
matter physics
Ross McKenzie
condensedconcepts.blogspot.com
• 1. to 11. review of key concepts from
thermodynamics
• 12. to 20. what I hope I will help you learn
1. Thermodynamics is powerful
• It gives a quantitative description of the
relationship between different physical
properties of diverse states of matter, e.g.,
gases, rubber, magnets, proteins,
superconductors, hot chocolate, ….
• In spite of complete ignorance about what
is happening at the atomic and molecular
level.
2. Equilibrium states
• Thermodynamics ONLY describes states
in thermal, mechanical, diffusive, and
chemical equilibrium, i.e., they do not
change with time.
3. State variables
• Only a small number of variables are
needed to completely specify a particular
equilibrium state (e.g., just pressure and
density for a gas).
• A state function has a unique value for any
given equilibrium state.
4. Adiabatic isolation and
irreversibility.
• A system is adiabatically isolated if its state is
unchanged by changes in its environment. Then
only mechanical means can be used to change
the state of the system.
• A process involving a change in state
A→B is irreversible for an adiabatically isolated
system if it is impossible to return the system to
state B, i.e., A is not accessible from B.
5. The second law and entropy
• For an adiabatically isolated system there
is a unique ordering of all possible
equilibrium states in terms of their relative
accessibility. (A→B→C→D…)
• This allows us to define a state function,
ENTROPY, s(A)<s(B)<s(C)<s(D)…
• The entropy of an isolated system can
never decrease.
6. The zeroth law and temperature
• If system X is in thermal equilibrium with Y, and
Y is in thermal equilibrium with Z, then X must
be in thermal equilibrium with Z.
• This allows us to define a state function
temperature.
• Temperature tells us whether or not two systems
will change when brought into thermal contact
with one another.
• A thermometer is just a very small system with
only one state variable.
7. First law and the internal energy
• For an adiabatically isolated system the
work done to move between two states is
independent of the path taken or process
used.
• This allows definition of a state function,
the internal energy, U.
• Q = ΔU + W is the definition of heat for a
process in a system which is not
adiabatically isolated.
8. Absolute temperature T and
absolute entropy S
• These are defined so that the (absolute)
entropy is an extensive state function.
S (A U B) = S(A) + S(B)
For a reversible process
dQ = T dS
9. TdS = dU +pdV
•
•
•
•
Combines zeroth, first, and second laws
Starting point for everything quantitative…
Entropy isRmeasurable.
T C (T )dT=T
v
T
S(T,V) =
where T0,V0 is a reference state assigned
zero entropy.
• Values of S for a material in a specific state
can often be looked up in data tables.
0
10. Free energy
• Helmholtz, A(V,T) = U – T S
• Gibbs, G(P,T) = U + PV – TS
• Second law: for a system in equilibrium
with an environment at fixed temperature
and pressure, G can never increase.
• G(T,P) must be a minimum.
11. dG = -SdT + VdP
• Maxwell relations
Where we are heading
• Intro to condensed matter physics
• Read
Schroeder, Thermal Physics, Section 5.3
Following slides are what I hope you will
learn
12. Phase diagrams
• P-T
• T-V
• T-x
13. Entropy vs. Energy
• Phase transitions occur because of this
competition.
• Generally decreasing the temperature
leads to transitions to phases with lower
internal energy and lower entropy.
14. Clausius-Clapeyron relation
• For first-order phase transitions
15. The critical point
• Universality: many apparently different
systems have the same properties (esp.,
critical exponents) near the critical point.
• van der Waals equation of state can be
used to obtain a semi-quantitative
description of the liquid-gas transition
16. Order parameters and
symmetry breaking
• A continuous (i.e., not first-order) phase
transitions occurs at a critical point.
• Almost all phases of matter are associated
with a broken symmetry.
• The order parameter is a measure of how
much the equilibrium state, below the
critical temperature, breaks the original
symmetry.
17. Ginzburg-Landau theory
• Gives a semi-quantitative understanding of
critical behaviour and continuous phase
transitions in terms of the dependence of
the Gibbs free energy on the order
parameter.
• Gives universal critical exponents.
• But, the exponents do not depend on n or
d, and disagree with experiment.
18. Entropy of mixing
19. Chemical equilibrium
• Due to the entropy of mixing chemical
reactions never proceed to completion.
• The equilibrium constant K defines the
relative concentrations of the reactants
and products in chemical equilibrium.
• ΔrGӨ ΔrHӨ, and ΔrSӨ can be determined
from K and its temperature dependence.
• All thermodynamic functions are defined
relative to a standard (reference) state.
20. The third law
• As the temperature tends to absolute zero
the entropy of the system becomes
independent of the state of the system
(e.g., independent of pressure, magnetic
field).
• You can never get to absolute zero.