Thermodynamics

Question 1

Molecular state

Answer 1

Molecular state is a quantum state of an individual molecule, that is, how the molecule distributes its energy in its different degrees of freedom.

Question 2

Microstate

Answer 2

A microstate is a possible distribution of the total energy among the molecules. (different possible distributions in energy level diagram)

Question 3

Configuration

Answer 3

A configuration is a possible distribution of the molecules among the molecular states. A configuration is a set of such occupation numbers.
E.g. configuration can be written as n0 = 2, n3 = 1 for 2 particles in the ground state and 1 in the third (3 quanta) state.

Question 4

Which energy levels are occupied as (B in Boltzmann distribution formula):

• B is large
• B is small

Answer 4

• If B is large, only lowest energy levels will be occupied.
• If B is small, then higher energy levels (excited states) are occupied.
  B behaves like the inverse of temperature.
  B = 1/kT

Question 5

What is the Boltzmann distribution?

Answer 5

The Boltzmann describes the occupation numbers of a (large) system at equilibrium. A system not following a Boltzmann distribution is not at equilibrium, and cannot be said to have a temperature.

Question 6

What is the molecular partition function q(T)?

Answer 6

The molecular partition function is, roughly, the number of thermally accessible states per molecule.

Question 7

What happens to the molecular partition function q(T), as temperature increases, and at low temperatures (T -> 0)?

Answer 7

q(T) increases with increasing temperature.
If T -> 0, then q(T) -> 1 (all molecules are in ground state).
If T -> infinity, then q(T) -> the number of molecular states. That is, more (higher-energy) states are occupied as T increases.

Question 8

What determines whether or not the configuration corresponds to an equilibrium configuration?

Answer 8

Temperature - a property of equilibrium systems only

Question 9

What is the characteristic temperature?

What happens if the temperature (T) is:

• higher than the characteristic temperature
• lower than the characteristic temperature

Answer 9

A characteristic temperature is, roughly, the lowest temperature at which the first excited state is significantly populated.

At T&raquo_space; characteristic temp, many states are occupied.
- If many states occupied, partition function q(T)&raquo_space; 1.
At T &laquo_space;characteristic temp, only ground state is significantly occupied.
- If only ground state occupied, then q(T) -> g(e0) [degeneracy of ground state].

Question 10

Explain the high temperature approximation used for translational motions.

Answer 10

Complex summations over huge numbers so approximate the discrete values with a continuous function. We assume that very many states are occupied.

• T&raquo_space; characteristic temp for translational (many excited states occupied)
• approximate ground state to zero

Question 11

Define heat

Answer 11

Heat is waste or non-usable energy that contributes to a change in temperature.

Question 12

Define work

Answer 12

Work is usable energy, such as in expansion of gas.

Question 13

Define heat capacity at constant volume, Cv

Answer 13

The amount of energy required to raise the temperature of a body by 1K.

Question 14

What determines chemical equilibrium?

Answer 14

Chemical equilibrium is determined by the system adopting the configuration with the greatest number of microstates.

Question 15

What is entropy change?

Answer 15

Entropy change predicts the direction of spontaneous change in terms of heat flow and temperature (macroscopic observables).

Question 16

Entropy condition for:

• spontaneous process
• equilibrium

Answer 16

• Spontaneous process: ds > 0

- Equilibrium: ds = 0

Question 17

What does quasi-static mean?

Answer 17

The heat flow has to be slow enough so that the system moved incrementally from equilibrium state to equilibrium state.

Question 18

What are the corresponding particles of:

• U (energy)
• V (volume)
• N (number of particles)

Answer 18

U -> T (temperature)
V -> P (pressure)
N -> chemical potential

Question 19

List extensive (depends on the amount N) and intensive (depends only on type of matter and not the amount) properties.

Answer 19

Extensive: S (entropy), U (energy), V (volume)
Intensive: temperature, pressure, chemical potential
* Note: all molar quantities are intensive e.g. heat capacity is extensive, but molar heat capacity is intensive.

Question 20

What are the constraints that minimise Gibbs free energy?

Answer 20

Constant T (temperature) and P (pressure)

Question 21

What is the triple point?

Answer 21

The unique T and P where all three phases have the same G (Gibbs free energy).
All three phases can coexist in equilibrium.

Question 22

What is the critical point?

Answer 22

The point where liquid and gas free energies become indistinguishable.

Question 23

What do the coexistence lines represent and what does this mean for the conditions?

Answer 23

Coexistence lines represent sets of values of P and T where two phases have the same free energy, and can coexist.
This means the two phases are both stable (have equal lowest G) at equilibrium (dG = 0), and require equal chemical potential in the two phases.

Question 24

What does the Clapeyron equation show?

Answer 24

It gives the sloe of a coexistence line on a P=T graph in terms of the enthalpy and volume differences between the coexisting phases.

Question 25

Solutions that exhibit a negative deviation from Raoult’s Law

Answer 25

Partial pressure lowered, more stable (e.g. acetone + chloroform).
Results from additional attraction between unlike molecules that are greater than the attractions between like molecules in the liquid.

Question 26

Solutions that exhibit a positive deviation from Raoult’s Law

Answer 26

Partial pressure is raised, doesn’t mix well (e.g. ethanol + water).
Results from weaker attractions between unlike molecules than those between like molecules in the liquid.

Question 27

What are azeotropes?

Answer 27

At the points called azeotropes, gas and liquid coexist at the same composition.

Question 28

How do azeotropes affect separation by distillation?

Answer 28

Distillation is possible with a negative azeotrope (maximum in T). Ptot < ideal solution.

Distillation directs the vapour composition towards a positive azeotrope (minimum in T). No separation can be achieved. Ptot > ideal solution.