Lecture 4

Question 1

What is internal energy?

Answer 1

A sum of all energy contained within the system - kinetic and potential energy. Symbol U, unit J.

Question 2

What is entropy?

Answer 2

A measure of disorder, how energy is distributed. A positive entropy would mean the system has more disorder. Symbol S

Question 3

What is the first law of thermodynamics?

Answer 3

The internal energy of a system is constant and doesn’t change with external influences. Energy in the system cant be destroyed or created.

Question 4

Is the entropy higher if the energy is distributed between many modes or less?

Answer 4

Many

Question 5

What is the second law of thermodynamics?

Answer 5

Any spontaneous change is accompanied by an increase in entropy, in an isolated system.

Question 6

What can entropy help understand?

Answer 6

-Help understand the spontaneous direction of a reaction
-When a reaction is at thermodynamic equilibrium.

Question 7

When a system is at equilibrium what should delta G be? (only at a constant temp and pres)

Answer 7

Equal to 0. If the reaction is spontaneous, G < 0. If G > 0 its spontaneous in the reverse reaction.

Question 8

What is the formula for G?

Answer 8

G = U + PV - TS
As enthalpy is equal to U + PV, G simplifies too
G = H - TS
Units are J for H and G.

Question 9

What is the unit for entropy, enthalpy and gibbs free energy.

Answer 9

S - J/K
H - J
G - J

Question 10

What is K? and how is it related to GFE?

Answer 10

K is the equilibrium constant and can be related with;
DeltaG = -RT lnK
DeltaG = -RT ln([reac]^coef/[prod]^coef)

Question 11

What is the formula for K?

Answer 11

Products^(coef)/Reactants^(coef)

(In concs)

Question 12

When a system is at constant temp and volume (V instead if P) what changes?

Answer 12

G becomes “Helmholtz free energy”, A, (in J).
Enthalpy is replaced with U

A = U - TS

Question 13

What is heat capacity (C) and how does it relate to U?

Answer 13

How much energy is needed to raise the temperature by a given units.

C = DeltaU/DeltaT

Question 14

Reminder, what does the MPF SHOW? and when is it relevant?

Answer 14

-Contains all thermody info about a system of independent particles at equilibrium
-Indicates the no of energy states accessible at a given temp
-Only relevant for systems with independent molecules and weakly coupled.

Question 15

What happens to the MPF when intermolecular forces need to be accounted for?

Answer 15

becomes Q.

Question 16

What is a thermodynamic ensemble?

Answer 16

Where certain parameters are fixed and is a collection of imaginary replicas of a system.

Question 17

What is a CONICAL ensemble?

Answer 17

Volume (V), composition (N) and temp (T) are fixed, with “N” particles.
All of the particles are considered to be in contact, so are all at the same T.
The energy levels available to the particles in each replica are the same (as fixed volume).
The total energy of the ensemble is the same but each replica can exchange energy. Replica energy isn’t fixed! only the full thing is.
As replicas can exchange energy there are many possible configs that give the total energy.
Some configs are most likely than others.

Question 18

What is the isothermal ensemble?

Answer 18

The same but P is exchanged for V.

Question 19

How can the statistical weight for each ensemble be calculated?

Answer 19

“W” = “N”!/”N1!”,”N2”!…

Where “N!” is the total number of members in the ensemble
“N1!” is the number of members of the ensemble with that specific energy.

Question 20

When “N” (the number of replicas in the full system) approaches infinity, what happens?

Answer 20

One config dominates.

Question 21

How is the dominant config found?

Answer 21

By maximising “W” under the constraints that the total energy “E” and the total number of ensembles “N” is constant.
Called the conical distribution and is very similar to the Boltzmann distribution.
“N”i/”N” = e^-Bie/Q

Question 22

What is the canonical partition function (Q)?

Answer 22

Sum(i)e^-BEi (only diff is a capital E)
Ei is the energy of a given replica
and the sum is over all replicas in the ensemble
So the top of the equation is for a specific replica (all that have that energy) and the bottom is all over them added up (over the full system)

Question 23

What is the density of states?

Answer 23

Number of states of in an energy range divided by the width of the range (no of states per energy unit)
This represents that the likeness of all energy being in 1 state is unlikely - most members have similar energy - due to 2 factors which are the exponential (making low states favoured) and that as energy is increased there are more states (higher states favoured)

Question 24

What is the mean energy equation with respect to Q?

Answer 24

By combining overall emergy (“E” = Sum(i)”N”iEi) with mean energy [E] = “E”/”N” we get
[E] = Sum(i)Ei”Ni”/”N”
then by subbing in the CPF
[E] = 1/QSum(i)Eie^-BEi
this can then be simplified to
[E] - 1/Q x dQ/dB
[E] = -(dellnQ/delB)V

Question 25

When is Q valid?

Answer 25

For real systems, with intermolecular interactions.

Question 26

How is q and Q linked?

Answer 26

Q = q^v

Where the v is equal to how many molecules are on the replica
THIS IS ONLY FOR DISTINGUISHABLE MOLECULES

Question 27

What is the formula when molecules are indistinguishable?

Answer 27

Q = q^v/N!

Question 28

What are the general rules about which molecules are distinguishable?

Answer 28

-All atoms/molecules of different kinds are distinguishable as they have diff weights.
-Atoms/molecules in a solid crystal lattice are always.
-Atoms/molecules in the gas phase are always indistinguishable (uncertainty principle)