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View on Cold in 17 th Century …while the sources of heat were obvious – the sun, the crackle of a fire, the life force of animals and human beings – cold was a mystery without an obvious source, a chill associated with death, inexplicable, too fearsome to investigate. - PowerPoint PPT Presentation
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View on Cold in 17th Century
…while the sources of heat were obvious – the sun, the crackle of a fire, the life force of animals and human beings
– cold was a mystery without an obvious source, a chill associated with death, inexplicable, too fearsome to
investigate.
“Absolute Zero and the Conquest of Cold” by T. Shachtman
• Heat “energy in transit” flows from hot to cold: (Thot > Tcold)
• Thermal equilibrium “thermalization” is when Thot = Tcold
•Arrow of time, irreversibility, time reversal symmetry breaking
Zeroth law of thermodynamics
A C
B C
Diathermal wall
If two systems are separately in thermal equilibrium with a third system, they are in thermal equilibrium with each other.
C can be considered the thermometer. If C is at a certain temperature then A and B are also at the same temperature.
Simplified constant-volume gas thermometer
Pressure (P = gh) is the thermometric property that changes with temperature and is easily measured.
Temperature scales
• Assign arbitrary numbers to two convenient temperatures such as melting and boiling points of water. 0 and 100 for the celsius scale.
• Take a certain property of a material and say that it varies linearly with temperature.
X = aT + b
• For a gas thermometer:
P = aT + b
-300 -200 -100 0 100 200
-273.15 oCPr
essu
re
Temperature (oC)
Gas Pressure ThermometerGas Pressure Thermometer
Steam point
Ice point
LN2
P = aP = a[[TT((ooC)C) + + 273.15]273.15]
Gas Pressure ThermometerGas Pressure Thermometer
Celsius scale
Steam point
Ice point
LN2
-300 -200 -100 0 100 200
-273.15 oCPr
essu
re
Temperature (oC)
Phase diagram of water
Near triple point can have ice, water, or vapor on making arbitrarily small changes in pressure and temperature.
Guillaume Amonton first derived mathematically the idea of absolute zero based on Boyle-Mariotte’s law in 1703.
Concept of Absolute Zero(1703)
Amonton’s absolute zero ≈ 33 K
For a fixed amount of gas in a fixed volume,
p = kT
Other Types of ThermometerOther Types of Thermometer
•Metal resistor : R = aT + b•Semiconductor : logR = a blogT•Thermocouple : = aT + bT2
Low Temperature ThermometryLow Temperature Thermometry
0 50 100 150 200 250 300 350 4000
50
100
150
R (
)
T (K)
Platinum resistance thermometer
0 100 200 300 400
100
1000
10000
R (
)
T (K)
CERNOX thermometer
International Temperature Scale of 1990
16 different configurations (microstates), 5 different macrostates
microstate Prob. (microstate) Macrostates: n,m Macrostate: n-m
hhhh 1/16 4, 0 4
thhh 1/16 3, 1 2
hthh 1/16 3, 1 2
hhth 1/16 3, 1 2
hhht 1/16 3, 1 2
tthh 1/16 2, 2 0
thth 1/16 2, 2 0
htht 1/16 2, 2 0
hhtt 1/16 2, 2 0
htth 1/16 2, 2 0
thht 1/16 2, 2 0
httt 1/16 1, 3 -2
thtt 1/16 1, 3 -2
ttht 1/16 1, 3 -2
ttth 1/16 1, 3 -2
tttt 1/16 0, 4 -4
Microcanonical ensemble:
• Total system ‘1+2’ contains 20 energy quanta and 100 levels.• Subsystem ‘1’ containing 60 levels with total energy x is in equilibrium with subsystem ‘2’ containing 40 levels with total energy 20-x.• At equilibrium (max), x=12 energy quanta in ‘1’ and 8 energy quanta in ‘2’
Ensemble: All the parts of a thing taken together, so that each part is considered only in relation to the whole.
The most likely macrostate the system will find itself in is the one with the maximum number of microstates.
E1
1(E1)
E2
2(E2)
TkdEd
dEd
B
1lnln
2
2
1
1
Most likely macrostate the system will find itself in is the one with the maximum number of microstates. (50h for 100 tosses)
0
2e+028
4e+028
6e+028
8e+028
1e+029
1.2e+029
0 20 40 60 80 100xMacrostate
Num
ber o
f Mic
rost
ates
()
E
(E)
Microcanonical ensemble: An ensemble of snapshots of a system with the same N, V, and E
A collection of systems thateach have the same fixed energy.
Canonical ensemble: An ensemble of snapshots of a system with the same N, V, and T (red box with energy << E. Exchange of energy with reservoir.
E-
(E-)
I()
1 1
1
1
1
1
1
11
1
1 1
1
1
1
1
1 1
1
1
1 1
1
1
1
1
1
1
1
1
1
1
1 1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1 1
1
1
1
1
1
1
1 1
1
1
1
11
1
1
1
1
1
1
1
1
1
1 1
1
1
1
1
1
1
1
1
1
1 1
1
11
1
1
1
1 1
1
1
1
1
1
1
1
11
1
Canonical ensemble: P() (E-)1 exp[-/kBT]
• Total system ‘1+2’ contains 20 energy quanta and 100 levels.• x-axis is # of energy quanta in subsystem ‘1’ in equilibrium with ‘2’• y-axis is log10 of corresponding multiplicity of reservoir ‘2’
Log 1
0 (P
())