View on Cold in 17th Century

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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 gt Tcold)
• Thermal equilibrium thermalization is when
  Thot Tcold
• Arrow of time, irreversibility, time reversal
  symmetry breaking

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Zeroth law of thermodynamics
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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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Gas Pressure Thermometer
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Gas Pressure Thermometer
Celsius scale
P aT(oC) 273.15
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Concept of Absolute Zero (1703)
Guillaume Amonton first derived mathematically
the idea of absolute zero based on
Boyle-Mariottes law in 1703.
For a fixed amount of gas in a fixed volume,
p kT
Amontons absolute zero 33 K
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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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Other Types of Thermometer

• Metal resistor R aT b
• Semiconductor logR a - blogT
• Thermocouple E aT bT2

Low Temperature Thermometry
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Platinum resistance thermometer
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CERNOX thermometer
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International Temperature Scale of 1990
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• In-class Exam 1, Wednesday, Feb 1 (50 minutes)
• Covers chapters 1-3, HW_A and lecture material.
• Formula sheets/notes (2 pages single sided)
  allowed.
• Hand held calculators allowed.
• HW_B will be posted Wed. , 1/25 (due, Friday,
  Feb 10)

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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
16 different configurations (microstates), 5
different macrostates
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Microcanonical ensemble

• Total system 12 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), x12 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.
E2 ?2(E2)
E1 ?1(E1)
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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)
Number of Microstates (?)
Macrostate
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Microcanonical ensemble An ensemble of snapshots
of a system with the same N, V, and E
A collection of systems that each 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 ? ltlt E. Exchange of energy with reservoir.
E-? ?(E-?)
? ?I(?)
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Canonical ensemble P(?) ? ?(E-?)?1 ? exp-?/kBT
Log10 (P(?))

• Total system 12 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