6d Flashcards
what is gibbs
the max amount of energy available to do work
G =
U + PV - TS
= H - TS
going from change in gibbs,, to change in gibbs equilibrium,, u get the
min
going from change in entropy,, to change in entropy at equilibrium u get
max
molecules contain // come with what
they come with energy levels
in an equilibrium system,, U,, internal energy depends on what
it depends on temperature
okay so if a molecule has energy leevls, and the U =3,, what do u do
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.
okay but which conformation represents // accounts for the equilibrium state.
the lowest energy state
every particle has what
every particle has a wavefunction associated with it
wavefunction total =
sum of particle wavefunctions
wavefunction new total =
when u switch 2 particles around and thereofore
ur keeping the positions the same but swapping the particles and their wavefunctions
how can we find out which conformation contributes to the equilibrium state more.
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.
okay so we have 2 particles and 2 different energy levels: how many different ways can we arrange the atoms across the energy levels
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
are some particle configurations more probable than others
yessss
the more probable ones occur most frequently
and make up the equilibrium state more.
the probability of a configuration is proportional to what
the number of microstates, W.
the probability of a configuration is proportionate to the number of microstates,, what must remain constant tho
the number of particles and energy must be constant
when entropy is at its max,, what change is equal to 0
when entropy is at its max,, change in on conformations probability is 0.
when u change a particles distribution,, what can P,, aka probability be changed into
it can be changed to ln(P)
when u change a particles probability distribution,, what must stay the same
number of particles
energy
their changes = 0
P,, probs,, can be changed to ln(p)
by changing distribution,, what do we do
we move further away from the max // minimum
what equation do we want to be a max
d ln(P) / dni
we want this to be a max!!!
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
(dln(p) / dni + a + B Ei ) change ni = 0
where a –> ni is constant particles
and BEi –> change ni is constant energy
what does ni(Ei) mean and what does it help us do
the number of particles at energy level ‘i’
helps us find W. (microstates)??
S in terms of S1 and S2
S = S1 + S2
W in terms of w and n
W = W1 x N2
S in therms of kb and w
S = KB ln(W)
what needs to be determined
alpha and beta,, bc theyre present in equations but we dk their values.
how do we find alpha’s value
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
No = what
long u total.
so total chemical potential ?
ni =
number of particles at energy level ‘i’.
ni = no e^beta Ei.
ni = in terms of boltzman distribution
ni = no, pi, exp( -Ei / KT)
N =
sum of Ni. (aka number of particles at energy level: i)
no =
ni / pi exp( -Ei / KT )
ni = in terms of q
N pi exp( -Ei / KT) / q
what does q equal =
sum of pi exp(-Ei/KT)
what is the acc meaning of q tho
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!!
