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. “Absolute Zero and the Conquest of Cold” by T. Shachtman Heat “energy in transit” flows from hot to cold: (T hot > T cold ) Thermal equilibrium “thermalization” is when T hot = T cold Arrow of time, irreversibility, time reversal symmetry breaking

Zeroth law of thermodynamics AC BC 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

Gas Pressure Thermometer Steam point Ice point LN 2

P = a[T( o C) ] Gas Pressure Thermometer Celsius scale Steam point Ice point LN 2

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 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 Thermometer Metal resistor : R = aT + b Semiconductor : logR = a  blogT Thermocouple : E = aT + bT 2 Low Temperature Thermometry Low Temperature Thermometry

Platinum resistance thermometer

CERNOX thermometer

International Temperature Scale of 1990

16 different configurations (microstates), 5 different macrostates microstateProb. (microstate)Macrostates: n,mMacrostate: n-m hhhh 1/164, 04 thhh 1/163, 12 hthh 1/163, 12 hhth 1/163, 12 hhht 1/163, 12 tthh 1/162, 20 thth 1/162, 20 htht 1/162, 20 hhtt 1/162, 20 htth 1/162, 20 thht 1/162, 20 httt 1/161, 3-2 thtt 1/161, 3-2 ttht 1/161, 3-2 ttth 1/161, 3-2 tttt 1/160, 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. E 1  1 (E 1 ) E 2  2 (E 2 )

Most likely macrostate the system will find itself in is the one with the maximum number of microstates. (50h for 100 tosses) Macrostate Number of Microstates (  )

E  (E) 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.

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()I()

Canonical ensemble: P(  )   (E-  )  1  exp[-  /k B T] 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 log 10 of corresponding multiplicity of reservoir ‘2’ Log 10 (P(  ))