ch273 stat mech knowledge

Question 1

liouville theorem

Answer 1

the volume of phase space occupied by an ensemble does not change in time
number of configs and density stays the same
shape of the ensemble dist function can change

Question 2

define ensemble

Answer 2

a collection of configurations of the macroscopic system
these configs are described by the same set of microscopic interactions and share as a whole common set of macroscopic properties

Question 3

principle of equal a priori probability

Answer 3

an isolated system is equally likely to be in any of the configurations of the ensemble

Question 4

NVE ensemble

Answer 4

-microcanonical
-fixed Number of particles
-fixed Volume
-conserved Energy (cannot exchange energy with its surroundings)

Question 5

what does conserved energy mean

Answer 5

total amount of energy in the system never changes

Question 6

what is the partition function

Answer 6

the total number of microscopic states (or configs) that the system can access

Question 7

what is the ensemble distribution function

Answer 7

where the configs of the ensemble are at a certain point of time

Question 8

define ergodic principle

Answer 8

the time averages are equal to the ensemble averages
time averages do not depend on the starting point
for a long enough time, the system can explore all the accessible phase space

Question 9

define entropy

Answer 9

measure of the number of of possible microscopic states of a system in thermodynamic equilibrium

Question 10

NVT ensemble

Answer 10

-canonical
-fixed N particles
-fixed Volume
-Temperature is conserved
-system is not isolated (heat transfer occurs)
-principle of a priori probability does NOT hold
-hamiltonian is not conserved

Question 10

types of elementary particles?

Answer 10

fermions and bosons

Question 10

what are fermions

Answer 10

-half integer spin (eg. electrons)
-two identical fermions cannot exist in identical states (pauli exclusion principle)

Question 10

what are bosons

Answer 10

-integer spin (eg photons)
-two identical bosons can occupy the same state

Question 10

virial equation of state definition

Answer 10

accounts for the deviations from the ideal behaviour via a power series in p

Question 11

what is g(r)

Answer 11

-radial distribution
-the probability of finding the centre of a particle from a given distance of the centre of another particle (reference)

Question 11

hard sphere potential

Answer 11

-assume the molecules are hard spheres
-infinitely repulsive (molecules can touch but not overlap)
-virial coefficients known up to at least B7(T)

Question 11

square well potential

Answer 11

-particles touch at σ
-when the potential is negative there are attractive interactions between the particles

Question 11

lennard jones potential

Answer 11

-combination of hard sphere and square-well

Question 12

what is the potential of mean force felt by n molecules in a liquid containing N molecules

Answer 12

the potential that generates the mean force felt by n molecules when the posititions of the remaining N-n molecules are canonically averaged over all possible configs of the liquid

Question 13

why would a total wavefunction to describe a molecule be antisymmetric?

Answer 13

-nuclei has a spin of 1/2
-meaning they are fermions
-therefore total wavefunction is antisym

Question 14

why do we only consider the electronic ground state when calculating the electronic partition function

Answer 14

excited states are usually separated from the grounf state by a few eV (which is a huge gap)
this leads to negligble terms in the electronic partition function