8d

Question 1

whats ni

Answer 1

number of particles in the energy level ‘i’

Question 2

we want to find the relationship of ni and N

aka the number of particles in energy level, ‘i’ and the total number of particles , how is this done §

Answer 2

by looking at q

Question 3

what is q

Answer 3

partition coefficient

works as a distribution normalisation at a given temp, T for a given set of energies, Ei.

kinda also describes a system in terms of micro states.

where a microstate is basiclaly just particles in different energy levels.

Question 4

q =

Answer 4

sum of: pi e( -Ei / KT)

this describes a system in terms of microstates.

Question 5

kinetic theory of gases gives us what equation

Answer 5

1/2 m<v> ^2 = 3/2 KbT</v>

Question 6

movement in every direction contributes how much

Answer 6

1/2 KBT

Question 7

what does < > mean

Answer 7

average velocity of all particles

means that several energy levels can be occupied or visited.

Question 8

<1/2 m v^2 > = what other 2 equations

Answer 8

1/2 m <v^2>

3/2 KBT

Question 9

q helps us find what

Answer 9

Q

Question 10

what can eb found usuig Q

Answer 10

u can find S and U
entropy and internal energy

Question 11

N ,, total number particals equals what

Answer 11

it equals the sum of ni

Question 12

boltzman population equation for non degenerative energy levels =

Answer 12

Ni/Nj = exp(-Ei/KT) / exp (-Ej/KT)

= exp -(Ei-Ej) / KT

Question 13

boltzman distribution for degenerative energy levels

Answer 13

Ni/Nj = gi/gj exp ( -(Ei-Ej) /KT) )

Question 14

what is Q

Answer 14

Q is the molar partition function

Question 15

q doesnt relate to the number of particles there is ,, but it does relate to what

Answer 15

it relates // contains the different energy levels.

Question 16

q = molecular or molar

Answer 16

molecular

Question 17

Q is molecular or molar

Answer 17

molar

Question 18

Q = q^N relates to what

Answer 18

the molar partition function when u have a distinguishable set of particles

aka in a solid or liquid ig.

an assembled set of atoms

Question 19

Q = q^N / N! relates to what

Answer 19

it relates to particles that are indistinguishable

aka not assmebled such as in a gas etc

Question 20

Q = q^N / N! is used for indistinguishable particles and canhelp us find what

Answer 20

it can help us find the specific heat from a statistical approach

Question 21

energy levels in a system can eb what

Answer 21

they can be spaced out largely or close together

Question 22

what does thr spacing between energy levels and the enrgy gap between them alter

Answer 22

it alters the amount of partices that will populate the larger energy levels.

aka the ones further away fro mthe ground state

Question 23

if energy levels are close together,, what is the effect

Answer 23

q will be larger
bc more energy levels will be populated
theres enough thermal energy to promote a bunch of energy levels

Question 24

if energy levels are far apart from eachother,, what does this do

Answer 24

it makes it harder to populate the higher energy leveks, ,the ones further away fro mthe ground state,, bc theres not enough thermal energy to do so.

Question 25

larger q =

Answer 25

close together energy levels lots of higher energy levels will also be populated!!

Question 26

small q

Answer 26

further away energy levels most of the energy levels will be populated near the groudn state!!

Question 27

when energy levels are spaced further apart and particles cant be prototed to themm,, whats the relationship between Ei and Kt

Answer 27

Ei >>>> KT which is why they cant be promoted,, bc even with an increase in temp,, the Ei is still too large to be overcome.

Question 28

ni when Ei >> Kt is what

Answer 28

around 0

Question 29

ni when u increase T

Answer 29

ni is no longer similar to 0. bc Ei is more populated bc. EI >> KT but increasing T makes KT more similar to Ei. allowing it to be populated as increase in T means more thermal energy for promotion.

Question 30

what does q do then

Answer 30

measures how much particles are spread over energy levels that are not the ground state

Question 31

q values can range from what to what,, and what influences its value

Answer 31

it can range from 0 --> 1 or very large numbers temp influences its value the larger the temp ,, the larger the value of q.

Question 32

large separattion is noemally seen between what

Answer 32

diff vibrational states of diatomic molecules

Question 33

a smaller separation is normally seen between what

Answer 33

translational energy levels // DOF

Question 34

okay so describe a graph where diff 🔺E are plotted. y axis = fractional occupation x axis = energy level

Answer 34

small 🔺E = flatish slope / line ,, theres a low fractional occupation across a range of different enrgy levels large 🔺E = steep slope. lower energy levels = larger fractional occupation,, larger enrgy levels have basically no fractional occupation!! so this means that for large 🔺E,, higher energy levels arent rlly populated!! just the ones closer to the ground state are populated.

Question 35

S long eqution

Answer 35

S = k(N ln(N) - alphaN - betaU)

Question 36

e(alpha) = what

Answer 36

n0 = N/q

Question 37

alpha =

Answer 37

ln(N) - ln(q)

Question 38

beta =

Answer 38

- 1/KT

Question 39

S for a distinguishable particle

Answer 39

S = k ln( q^N) + U/T in a crystalline solid

Question 40

high U valuse must be assocated with what

Answer 40

the population of higher energy levels of translational or vibrational nature.

Question 41

how does u link to q,, and what do we want to remove from thr equation

Answer 41

we want to remove Ei fro mthe equation by substituting in the q values depending on if its a distinguishable or undistinguishable particle. U = (NKT^2 / q) (dq/dT) = KT^2 d ln(Q) / dT

Question 42

okay so yes q, is the partition function,, but what acc is it

Answer 42

it contains all the info that. describes the equilibrium state of a system

Question 43

whats this all about in terms of particles

Answer 43

how the particles are distributed over energy levels + whether those particles are localised (crystal) or delocalised (gas)

Question 44

translational partition function =

Answer 44

mv = nh / 2L

Question 45

kinetic energy =

Answer 45

1/2mv^2 = n^2 h^2 / 8mL^2

Question 46

En from schrodinger =

Answer 46

En = n^2 pi^2 h.dash^2 / 2mL^2 n = 1,2,3 etc

Question 47

what is particle in a box about

Answer 47

a particle being confined by an infinate potential well of width L.

Question 48

q trans 1D for 1D motion =

Answer 48

sum of exp ( -n^2 h^2 / 8mL^2 KT) energy levels are closely spaced tho so exp ( -n^2 h^2 / 8mL^2 KT) dn x^2 = ( -n^2 h^2 / 8mL^2 KT) = root ( 2pi m K T) L / h

Question 49

for 3D motion,, each x, y ,z contributes what ?? the same quantity or different

Answer 49

it contributes the same quantity !! so we just cube it. so ( root[ 2 pi m KT] L / h ) ^3

Question 50

L ^3 is what in particle in a box

Answer 50

L ^3 is thr volume of the box!!

Question 51

what happens to q as volume of box increases

Answer 51

q increases as the volume of the box increases. bc it determines energy levels in the particle in a box approach.

Question 52

how do we find U due to translational energy states.

Answer 52

U = NKT ^2 3/2 1/T = 3/2 NKT = 3/2 RT bc gas particles are indistinguishable making the Q and q relationship for 1 mole of gas molecules: (Q trans) 3d = 1/n! ((q trans) 3d) ^N.