Thermal Physics
• Too many particles… can’t keep track!
• Use pressure (p) and volume (V) instead.
• Temperature (T) measures the tendency of an object to
spontaneously give up/absorb energy to/from its
surroundings. (p and T will turn out to be related to the
too many particles mentioned above)
• p, V, and T are related by the equation of state: f(p,V,T) = 0
e.g. pV = NkBT
• Heat is energy in transit and it is somehow related to
temperature
Zeroth law of thermodynamics
A
C
If two systems are separately
in thermal equilibrium with a
third system, they are in
thermal equilibrium with each
other.
Diathermal
wall
B
C
C can be considered the
thermometer. If C is at a
certain temperature then A
and B are also at the same
temperature.
• Temperature is related to heat and somehow
related to the motion of particles
• Need an absolute definition of temperature based
on fundamental physics
• A purely thermal physics definition is based on the
Carnot engine
• Can also be defined by statistical arguments
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Microstates and Macrostates
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Microstates and Macrostates
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Microstates and Macrostates
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All these microstates belong to the macrostate of 1 head in 100 coins
Most likely macrostate the system will
find itself in is the one with the maximum
number of microstates.
Number of Microstates ()
1.2e+029
1e+029
8e+028
6e+028
4e+028
2e+028
0
0
20
40
x
Macrostate
60
80
100
n = 170;
x = 0:1:n;
y =
factorial(n)./(factorial(x).*fac
torial(n-x));
figure;
plot(x,y);
1.Each microstate is equally likely
2.The microstate of a system is
continually
changing
How is all this @#$%^&
3.Given
enough to
time,
the system
related
thermal
will explore all possible
physics?
microstates and spend equal time
in each of them (ergodic
hypothesis).
Big question:
How do we relate the number
of microstates for a particular
macrostate to temperature?
E1
+ E
T1 < T2
E2 - E
But no particular relation for E1 and E2
At thermal equilibrium the temperature (whatever it is) will be the same
for both systems. Total energy E = E1 + E2 is conserved.
clear all;
n1 = 4;
n2 = 8;
e = 6;
i = 0;
for x = 0:1:n1
y1 =(factorial(n1)./(factorial(x).*factorial(n1-x)));
y2 = (factorial(n2)./(factorial(e-x).*factorial(n2-(e-x))));
i=i+1;
y(i)=y1*y2
x1(i)=x;
end
figure;
plot(x1,y);
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0
0
0.5
1
1.5
2
2.5
3
3.5
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Most likely macrostate the system will find
itself in is the one with the maximum
number of microstates.
E1
E2
1(E1)
(E)
2(E2)
d ln 1 d ln  2
1


dE1
dE2
k BT
Ensemble: All the parts of a thing taken together,
so that each part is considered only in relation to
the whole.
E
(E)
Microcanonical ensemble:
An ensemble of snapshots
of a system with the same
N, V, and E
Microcanonical ensemble: An ensemble of
snapshots of a system with the same N, V, and E
Canonical ensemble: An ensemble of snapshots
of a system with the same N, V, and T
E1
1(E1)
E2
2(E2)