2. Intro to Statistical Mechanics Flashcards
What are the two approaches you can take to solving a problem?
Thermodynamics or S.M.
What does thermodynamics assume?
A unique normal state called thermal equilibrium
How many laws of thermodynamics are there, and which quantities do they relate?
4
- Relate p, V, T, S and V
pressure, volume, temp, entropy and volume
What type of laws are the thermodyamics laws?
Empirical laws judged experimentally
What quantities does S.M. define?
Entropy and thermal equilibrium in terms of microscopic probabilities
How does S.M. determine measureable properties?
Using averages over the probabilities of particular states
Define an isolated system, and state what quantites are fixed
The system cannot exhange with a reservoir
- Fixes the E, N and V
the energy, number of molecules and the volume
What is a microstate?
Any microscopic configuration of a system
How easy is the microstate to measure and give an example?
Very difficult - e.g. need to measure position and velocity of every molecule in a gas
What is a macrostate?
Any configuration with a particular measurable properties
State the relationship between a macrostate and a microstate
A macrostate often corresponds to many microstates
Give an example of a macrostate
The pressure, volume and internal energy for 1L of gas
What does S.M. assume about the possible microstates in an isolated system in thermal equilibrium?
They are all equally likely to occur
Why do a systems microstates constantly change?
Because of the system’s dynamics
State the Ergodic hypothesis
Given enough time, the system will explore and spend equal time in all possible microstates
Which macrostate will a system choose?
The one associated with the maximum number of microstates
How do you calculate the measured value of an observable?
By averaging over all the microstates
See page 2 of document for the 3 SHO example
Do it
Define the microcanonical ensemble
An ensemble of isolated systems with fixed energy, (and N and V)
Define the canonical ensemble
An ensemble of systems that can exchange energy with a large reservoir
Define the grand canonical ensemble
The same as the canonical ensemble, but can exchange energy and particles
Which important quantities are exchanged and fixed in the grand canonical ensemble?
- Energy and particles are exchanged
- Temperature and the chemical potential are fixed
