10.9: I- Catalog of Misconceptions

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Effective teaching does not simply teach students what is correct—it also insures that students do not believe what is incorrect. There are a number of prevalent misconceptions in statistical mechanics. For example, an excellent history of statistical mechanics is titled The Kind of Motion We Call Heat. This title is wonderfully memorable and historically justifiable, but it embodies no fewer than three different physics misconceptions: heat is confused with thermal energy; thermal energy is confused with kinetic energy; and kinetic energy is confused with motion. Below is a list of misconceptions that are explicitly mentioned in this book, together with the page number where that misconception is pointed out and corrected.

a microstate (a configuration) has an entropy, 32

all gases are ideal, 44

at high temperature, the most probable microstate has high energy, 107

balls-in-buckets picture of quantal states, 145, 158

Boltzmann distribution is for molecules within systems, 99, 104

Bose-Einstein “condensation”, 158

canonical probability for a quantal state that doesn’t have a definite energy, 113, 128

chemical potential increases with temperature, 46, 152, 153, 155, 168

computers are fast, 199

concerning (anti)symmetric functions, 144

concerning Monte Carlo simulation, 202

concerning multivariate calculus, 57

concerning quantum mechanics, 48

configurational entropy differs from thermal entropy, 52

C_p is ∂E/∂T)_p, 81

definition of partition function, 100

density is uniform at equilibrium, 7, 16, 45, 64

energy must be a function of (S, V, N), 68, 78

ensemble is a collection of atoms, 16

entropy as (moral?) decay, 30

entropy as disorder, 34

entropy doesn’t apply to a pendulum, 135

equation of state contains all thermodynamic information, 69, 88

heat is thermal energy, 50, 51

highest temperature implies maximum energy, 135, 136

ideal gas is hard-sphere gas, 21

ideal gas potential energy, 21, 102

in Reif, 48

occupancy probability vs. canonical probability, 149

one molecule is an ensemble element, 99, 104

phase diagram plots pressure as a function of temperature, 7

probability of atom having energy E is proportional to e^−E/k_BT, 104

sum over typical microstates, not over all microstates, 23, 100

temperature is energy per particle, 42

the most probable energy is the energy of the most probable microstate, 107

thermal energy is kinetic energy, 50, 51, 107