Statterm begreper

Conjugate variables

Variables/properties that appear in pairs, consisting of one intensive property (e.g. pressure) and one extensive property (e.g. volume), where the intensive property acts as a “driving force” since it is the same everywhere at equilibrium.

Common examples are pV and mu*N

Independent variables

Can change independently of each other, and are often controlled by being kept fixed.

Dependent variables

Need to be measured experimentally or calculated from the values of the independent variables.

Canonical ensemble

T, V, N

Adiabatic process

No heat flow, dq = 0

quasi-static process

Processes that are performed slow enough for their properties to be independent of time and the speed of the process. The process must be slower than the relaxation time of a system.

Maxwell’s relations

Relationships between partial derivatives of state functions. Useful because it gives us ways to get unmeasurable quantities from easily measured quantities.

Entropy

The measure of disorder in a system. Can be calculated using Boltzmanns law S = kblnW

Multiplicity (W)

All possible microstates of a system

reversible processes

Are quasi-static and happen in such a way that the combined entropy of the system and it’s surroundings is constant.

Ensemble

Refers either to a set of variables we are controlling, or the collection of all possible microstates of a system

Principle of maximum multiplicity

A system will change its degrees of freedom to reach a state of maximum multiplicity (entropy)

Microcanonical ensemble

S(U, V, N)

Driving force

Pushes a system towards equilibrium by maximizing the entropy (in terms of the microcanonical ensemble)

Response property

A property that describes how the system changes when it is pertrubed

Connecting the macroscopic and microscopic world

F = U - TS and F = -kTlnQ

The contributions to the molecular partition function

rotation, translation, vibration and electronic exitation

Connection between the total energy of the system and the internal thermal energy

They may differ with a chosen zero-point U0, so that E = U - U0.

The partition function

a sum over all possible states a system can be in/a sum of boltzmann factors. Increases with E and T.

Why we can ignore qe in the molecular partition function

At normal temperatures, only the electronic ground state will usually be occupied, which is usually not degenerate

Surface tension

The free energy cost of increasing the surface area of the system

Regular solution

A solution that does not behave as an ideal solution, and seeks to minimize the free energy and maximize the entropy

Ideal solution

Only driven by entropy, all molecular interactions are equal

Thermodynamic condition for a two-phase solution

The free energy of solution must have two minima. The interface tension must be positive and large enough to dominate the entropy terms.

The multiplicity of a dimer on a quadratic lattice with L² sites

W = 2L(L-1) =aprox 2L² if L is large

The hydrophobic effect

Large s-s interaction energy will cause two unpolar molecules to dimerize in water.

Colligative property

depends on the mole fraction and not on the nature of the chemical species

Solvent