2. Intro to Statistical Mechanics

Question 1

What are the two approaches you can take to solving a problem?

Answer 1

Thermodynamics or S.M.

Question 2

What does thermodynamics assume?

Answer 2

A unique normal state called thermal equilibrium

Question 3

How many laws of thermodynamics are there, and which quantities do they relate?

Answer 3

4
- Relate p, V, T, S and V
pressure, volume, temp, entropy and volume

Question 4

What type of laws are the thermodyamics laws?

Answer 4

Empirical laws judged experimentally

Question 5

What quantities does S.M. define?

Answer 5

Entropy and thermal equilibrium in terms of microscopic probabilities

Question 6

How does S.M. determine measureable properties?

Answer 6

Using averages over the probabilities of particular states

Question 7

Define an isolated system, and state what quantites are fixed

Answer 7

The system cannot exhange with a reservoir
- Fixes the E, N and V
the energy, number of molecules and the volume

Question 8

What is a microstate?

Answer 8

Any microscopic configuration of a system

Question 9

How easy is the microstate to measure and give an example?

Answer 9

Very difficult - e.g. need to measure position and velocity of every molecule in a gas

Question 10

What is a macrostate?

Answer 10

Any configuration with a particular measurable properties

Question 11

State the relationship between a macrostate and a microstate

Answer 11

A macrostate often corresponds to many microstates

Question 12

Give an example of a macrostate

Answer 12

The pressure, volume and internal energy for 1L of gas

Question 13

What does S.M. assume about the possible microstates in an isolated system in thermal equilibrium?

Answer 13

They are all equally likely to occur

Question 14

Why do a systems microstates constantly change?

Answer 14

Because of the system’s dynamics

Question 15

State the Ergodic hypothesis

Answer 15

Given enough time, the system will explore and spend equal time in all possible microstates

Question 16

Which macrostate will a system choose?

Answer 16

The one associated with the maximum number of microstates

Question 17

How do you calculate the measured value of an observable?

Answer 17

By averaging over all the microstates

Question 18

See page 2 of document for the 3 SHO example

Answer 18

Do it

Question 19

Define the microcanonical ensemble

Answer 19

An ensemble of isolated systems with fixed energy, (and N and V)

Question 20

Define the canonical ensemble

Answer 20

An ensemble of systems that can exchange energy with a large reservoir

Question 21

Define the grand canonical ensemble

Answer 21

The same as the canonical ensemble, but can exchange energy and particles

Question 22

Which important quantities are exchanged and fixed in the grand canonical ensemble?

Answer 22

• Energy and particles are exchanged

- Temperature and the chemical potential are fixed