Chapter 16 - Statistical Thermodynamics 1: The Concepts

Adiabatic demagnetization

- Based on that, in the absence of a magnetic field, the unpaired electrons of a paramagnetic material are orientated at random.

Thermal

wavelength- Decreases with increasing mass and temperature.

Adiabatic demagnetization

- Based on that, in the absence of a magnetic field, the unpaired electrons of a paramagnetic material are orientated at random.

Thermal

wavelength- Decreases with increasing mass and temperature.

Population

- The average number of molecules that occupy it.

Optical

trapping- Where atoms in the gas phase are cooled by inelastic collisions with photons from intense laser beams.

Sackur Tetrode

equation- It implies that the molar entropy of a perfect gas of high molar mass is greater than one of low molar mass under the same conditions.

priori probabilities

Principle of equal a(n) - The assumption that all possibilities for the distribution of energy are equally probable.

Canonical

ensemble- The imaginary collection of replications of the actual system with a common temperature.

Statistical thermodynamics

- The link between individual molecular properties and bulk thermodynamic properties.

Weight of the configuration

- The number of ways a general configuration can be achieved.

Canonical partition function

(Q)- A function of the temperature.

Statistical thermodynamics

The link between individual molecular properties and bulk thermodynamic properties

Population

The average number of molecules that occupy it

Principle of equal a priori probabilities

The assumption that all possibilities for the distribution of energy are equally probable

Weight of the configuration

The number of ways a general configuration can be achieved

Stirling's approximation

Boltzmann distribution

Molecular partition function

Common methods used to reach very low temperatures

• Optical trapping
• Adiabatic demagnetization

Optical trapping

Where atoms in the gas phase are cooled by inelastic collisions with photons from intense laser beams

Adiabatic demagnetization

Based on that, in the absence of a magnetic field, the unpaired electrons of a paramagnetic material are orientated at random

Thermal wavelength

Decreases with increasing mass and temperature

The total energy of the system relative to the energy of the lowest state

Boltzmann formula for the entropy

Canonical ensemble

The imaginary collection of replications of the actual system with a common temperature

Microcanonical ensemble

Where the condition of constant temperature is replaced by the requirement that all the systems should have exactly the same energy

Grand canonical ensemble

The volume and temperature of each system are the same, but they are open, which means that matter can be imagined as able to pass between the systems; the composition of each one may fluctuate, but the chemical potential is the same in each system

Canonical distribution

Canonical partition function (Q)

A function of the temperature

The total weight (W) of a configuration of the ensemble

The product of the average weight W of each member of the ensemble

For distinguishable independent molecules

For indistinguishable independent molecules

Sackur-Tetrode equation

It implies that the molar entropy of a perfect gas of high molar mass is greater than one of low molar mass under the same conditions