6d

Question 1

what is gibbs

Answer 1

the max amount of energy available to do work

Question 2

G =

Answer 2

U + PV - TS

= H - TS

Question 3

going from change in gibbs,, to change in gibbs equilibrium,, u get the

Answer 3

min

Question 4

going from change in entropy,, to change in entropy at equilibrium u get

Answer 4

max

Question 5

molecules contain // come with what

Answer 5

they come with energy levels

Question 6

in an equilibrium system,, U,, internal energy depends on what

Answer 6

it depends on temperature

Question 7

okay so if a molecule has energy leevls, and the U =3,, what do u do

Answer 7

u put the particles in energy levels that when u add,, they add up to 3.

and 1 in 0 and 1 in 3
or 1 in 2 and 1 in 1

the sum of enrgy levels must add up to the internal energy.

u put the particles in different conformations till they add up to 3. or the value of U.

Question 8

okay but which conformation represents // accounts for the equilibrium state.

Answer 8

the lowest energy state

Question 9

every particle has what

Answer 9

every particle has a wavefunction associated with it

Question 10

wavefunction total =

Answer 10

sum of particle wavefunctions

Question 11

wavefunction new total =

Answer 11

when u switch 2 particles around and thereofore

ur keeping the positions the same but swapping the particles and their wavefunctions

Question 12

how can we find out which conformation contributes to the equilibrium state more.

Answer 12

by looking at how many ways a number of particles (N) can be distributed over a certain number of energy levels.

remember that each particle has a different wavefunction so we can tell the diff between the particles.

Question 13

okay so we have 2 particles and 2 different energy levels: how many different ways can we arrange the atoms across the energy levels

Answer 13

4!!

2 on the lower
1 up 1 down
1 down 1 up
2 on the upper

we can distinguish between the the 2 particles so we can tell the diff between 1 up 1 down and 1 down 1 up. bc we know they have different wavefunctions

Question 14

are some particle configurations more probable than others

Answer 14

yessss
the more probable ones occur most frequently

and make up the equilibrium state more.

Question 15

the probability of a configuration is proportional to what

Answer 15

the number of microstates, W.

Question 16

the probability of a configuration is proportionate to the number of microstates,, what must remain constant tho

Answer 16

the number of particles and energy must be constant

Question 17

when entropy is at its max,, what change is equal to 0

Answer 17

when entropy is at its max,, change in on conformations probability is 0.

Question 18

when u change a particles distribution,, what can P,, aka probability be changed into

Answer 18

it can be changed to ln(P)

Question 19

when u change a particles probability distribution,, what must stay the same

Answer 19

number of particles
energy
their changes = 0

P,, probs,, can be changed to ln(p)

Question 20

by changing distribution,, what do we do

Answer 20

we move further away from the max // minimum

Question 21

what equation do we want to be a max

Answer 21

d ln(P) / dni

we want this to be a max!!!

Question 22

whats the full d ln(P) / dni equation.

we want this to be a max but theres extra stuff we neeed to add that account for the constant energy + constant particles

Answer 22

(dln(p) / dni + a + B Ei ) change ni = 0

where a –> ni is constant particles

and BEi –> change ni is constant energy

Question 23

what does ni(Ei) mean and what does it help us do

Answer 23

the number of particles at energy level ‘i’

helps us find W. (microstates)??

Question 24

S in terms of S1 and S2

Answer 24

S = S1 + S2

Question 25

W in terms of w and n

Answer 25

W = W1 x N2

Question 26

S in therms of kb and w

Answer 26

S = KB ln(W)

Question 27

what needs to be determined

Answer 27

alpha and beta,, bc theyre present in equations but we dk their values.

Question 28

how do we find alpha’s value

Answer 28

we set the ground state energy to Eo = 0

no = number of particles at energy level 0. (this is not degenerate (po=1)

therefore e ^alpha = number of particles at energy level o. aka no

so e^alpha = No

Question 29

No = what

Answer 29

long u total.

so total chemical potential ?

Question 30

ni =

Answer 30

number of particles at energy level ‘i’.

ni = no e^beta Ei.

Question 31

ni = in terms of boltzman distribution

Answer 31

ni = no, pi, exp( -Ei / KT)

Question 32

N =

Answer 32

sum of Ni. (aka number of particles at energy level: i)

Question 33

no =

Answer 33

ni / pi exp( -Ei / KT )

Question 34

ni = in terms of q

Answer 34

N pi exp( -Ei / KT) / q

Question 35

what does q equal =

Answer 35

sum of pi exp(-Ei/KT)

Question 36

what is the acc meaning of q tho

Answer 36

the partition function

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

this is the psychology distribution thing we learnt about in 6formmm. the curves with the mean, mode, median etccccc. this is what a distribution normalisation is.

and q gives us this at a given set of energies!!