view on cold in 17 th century
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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 PresentationTRANSCRIPT
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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
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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.
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Simplified constant-volume gas thermometer
Pressure (P = gh) is the thermometric property that changes with temperature and is easily measured.
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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
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-300 -200 -100 0 100 200
-273.15 oCPr
essu
re
Temperature (oC)
Gas Pressure ThermometerGas Pressure Thermometer
Steam point
Ice point
LN2
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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)
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Phase diagram of water
Near triple point can have ice, water, or vapor on making arbitrarily small changes in pressure and temperature.
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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
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Other Types of ThermometerOther Types of Thermometer
•Metal resistor : R = aT + b•Semiconductor : logR = a blogT•Thermocouple : = aT + bT2
Low Temperature ThermometryLow Temperature Thermometry
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0 50 100 150 200 250 300 350 4000
50
100
150
R (
)
T (K)
Platinum resistance thermometer
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0 100 200 300 400
100
1000
10000
R (
)
T (K)
CERNOX thermometer
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International Temperature Scale of 1990
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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
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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’
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Ensemble: All the parts of a thing taken together, so that each part is considered only in relation to the whole.
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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
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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
()
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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.
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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()
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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
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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
())