Week 3 (15) Flashcards
(15 cards)
What are the two definitions of Chemical potential?
Chemical potential is the energy that ca be absorbed/released due to a change of particle number e.g in a chemical reaction or phase transition:
μ = (dU/dS)_V,N
or it is the Gibbs energy per particle for a homogeneous system:
μ = G/N
How do particles flow compared to chemical potenital?
particles flow from high to low potential energy, to try to equalise the potential
How does heat flow?
Heat flows from hotter to colder temperatures, to try to equalise the temperature.
What is specific volume and specific entropy?
the volume or entropy per particle:
v ̂ = V/N
s ̂ = S/N
what is latent heat?
Latent heat is the energy required to convert a liquid to gas or vice versa, without a change in temperature.
L = ΔQ
L is positive is heat is released
L is negative is heat is absorbed
What is special about water and why?
For most materials, the density of the solid phase is higher than the liquid phase, for water this is the opposite.
This is due to the hydrogen bonding between water molecules.
What is the 3rd law of thermodynamics?
Entropy of all systems in internal equilibrium tends to a constant at absolute zero, and so may be taken as zero (S=0 at T=0)
What are 3 consequences of the 3rd law?
- All systems only have 1 available state at T=0 (S=k_b ln(Ω))
- Heat capacity must be zero at T=0
- It is impossible to cool something to T=0 in a finite number of steps
What is a macrostate?
What is a microstate?
A macrostate is defined by the macroscopic properties of the system (temperature, pressure, volume, etc).
A microstate is a specific microscopic configuration of a system that may be occupied with a certain probability from its thermal fluctuations.
Microstates are the many different possible ways that a particular macrostate can be achieved.
What is a ensemble?
An ensemble is a large number of virtual copies of a system which are all the same but configured in random ways, for example
An ensemble average is the average state of all of these virtual systems, assumed if its:
- a single system over a long time, so it goes through all of the possible configurations.
- a large number of identical (but randomly configured) systems in a a short time
What are the 3 types of ensembles?
- Micro-canocical ensemble:
Isolated system with fixed U, V, N. e.g the whole gas - Canonical (standard) ensemble:
System is in contact with a thermal reservoir, V, N, T are all fixed (exchange heat, but not particles). e.g each atom in gas is a separate system, the rest of the gas is the reservoir. - Grand-canonical ensemble:
System can exchange heat and particles with the reservoir. V, T, μ
are all fixed. e.g a microstate of the configuration of the gas is a system, the rest of the gas is the reservoir.
What is the principle of equal equilibrium probability?
When a thermally isolated system comes into thermal equilibrium then the state probabilities of any set of mutually accessible states become equal.
In a microcanonical ensemble, there is equal probability of any state being occupied.
What is the Ergodic hypothesis?
Given enough time the systems will explore all possible microstates and will spend an equal amount of time in each of them.
This implies that in equilibrium, an isolated state will chose the macrostate with the most microstates (to maximise entropy - 2nd law).
What is the Boltzmann equation for entropy?
S = k_B lnΩ
What does the second law tell us about a systems number of states, Ω?
2nd law, system evolves to maximum S (entropy only increases), so system evolves to maximise the number of states Ω.
