Thermodynamics Flashcards
Molecular state
Molecular state is a quantum state of an individual molecule, that is, how the molecule distributes its energy in its different degrees of freedom.
Microstate
A microstate is a possible distribution of the total energy among the molecules. (different possible distributions in energy level diagram)
Configuration
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.
Which energy levels are occupied as (B in Boltzmann distribution formula):
- B is large
- B is small
- 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
What is the Boltzmann distribution?
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.
What is the molecular partition function q(T)?
The molecular partition function is, roughly, the number of thermally accessible states per molecule.
What happens to the molecular partition function q(T), as temperature increases, and at low temperatures (T -> 0)?
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.
What determines whether or not the configuration corresponds to an equilibrium configuration?
Temperature - a property of equilibrium systems only
What is the characteristic temperature?
What happens if the temperature (T) is:
- higher than the characteristic temperature
- lower than the characteristic temperature
A characteristic temperature is, roughly, the lowest temperature at which the first excited state is significantly populated.
At T»_space; characteristic temp, many states are occupied.
- If many states occupied, partition function q(T)»_space; 1.
At T «_space;characteristic temp, only ground state is significantly occupied.
- If only ground state occupied, then q(T) -> g(e0) [degeneracy of ground state].
Explain the high temperature approximation used for translational motions.
Complex summations over huge numbers so approximate the discrete values with a continuous function. We assume that very many states are occupied.
- T»_space; characteristic temp for translational (many excited states occupied)
- approximate ground state to zero
Define heat
Heat is waste or non-usable energy that contributes to a change in temperature.
Define work
Work is usable energy, such as in expansion of gas.
Define heat capacity at constant volume, Cv
The amount of energy required to raise the temperature of a body by 1K.
What determines chemical equilibrium?
Chemical equilibrium is determined by the system adopting the configuration with the greatest number of microstates.
What is entropy change?
Entropy change predicts the direction of spontaneous change in terms of heat flow and temperature (macroscopic observables).
Entropy condition for:
- spontaneous process
- equilibrium
- Spontaneous process: ds > 0
- Equilibrium: ds = 0
What does quasi-static mean?
The heat flow has to be slow enough so that the system moved incrementally from equilibrium state to equilibrium state.
What are the corresponding particles of:
- U (energy)
- V (volume)
- N (number of particles)
U -> T (temperature)
V -> P (pressure)
N -> chemical potential
List extensive (depends on the amount N) and intensive (depends only on type of matter and not the amount) properties.
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.
What are the constraints that minimise Gibbs free energy?
Constant T (temperature) and P (pressure)
What is the triple point?
The unique T and P where all three phases have the same G (Gibbs free energy).
All three phases can coexist in equilibrium.
What is the critical point?
The point where liquid and gas free energies become indistinguishable.
What do the coexistence lines represent and what does this mean for the conditions?
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.
What does the Clapeyron equation show?
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.
Solutions that exhibit a negative deviation from Raoult’s Law
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.
Solutions that exhibit a positive deviation from Raoult’s Law
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.
What are azeotropes?
At the points called azeotropes, gas and liquid coexist at the same composition.
How do azeotropes affect separation by distillation?
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.
