Statistical Mechanics

Question 1

What is the goal of statistical mechanics?

Answer 1

Statistical mechanics considers how particles occupy their allowed quantized energy states and is used to relate molecular behavior to macroscopic thermodynamics.

Boyd, NEGD, Pg 84

Question 2

Define the degree of molecular randomness.

Answer 2

The number of different ways that N particles can be distributed among their allowable quantum energy states without changing the total energy of the system E.

Boyd NEGD, Pg 84

Question 3

What is a “microstate?”

Answer 3

If we can arrange N particles in a system such that the total energy E does not change, that particular arrangement of particles is called a microstate.

Boyd NEGD, Pg 85

Question 4

Particles that have an even number of elementary units are called ______.

Answer 4

Bosons.

Boyd NEGD, Pg 85

Question 5

True or False
Bosons are analyzed using Bose-Einstein statistics.

Answer 5

True.

Boyd NEGD, Pg 85

Question 6

Give some examples of Bosons.

Answer 6

Hydrogen atoms
He^4
N_2
Photons

Boyd NEGD, Pg 85

Question 7

Particles made up of an odd number of elementary particles are called ______.

Answer 7

Fermions.

Boyd NEGD, Pg 85

Question 8

True or False
Fermions are analyzed using Bose-Einstein statistics.

Answer 8

False. They are analyzed using Fermi-Dirac statistics.

Boyd NEGD, Pg 85

Question 9

True or False
No two Fermions can occupy the same state.

Answer 9

True.

Boyd NEGD, Pg 85

Question 10

What are some examples of Fermions?

Answer 10

1. Electrons, protons, and He^3

Boyd NEGD, Pg 85

Question 11

True or False
For Bosons, there is no limit on the number of particles in each energy state.

Answer 11

True.

Boyd NEGD, Pg 88

Question 12

True or False
Bosons follow the Pauli exclusion principle.

Answer 12

False. Fermions follow this principle.

Wikapedia

Question 13

Give the general purpose of Bose-Einstein statistics.

Answer 13

Bose-Einstein statistics describe the statistical distribution of indistinguishable particles called bosons that can occupy the same quantum state.

chatGPT

Question 14

What is the general purpose of Fermi-Dirac statistics?

Answer 14

The purpose of Fermi-Dirac statistics in statistical mechanics is to provide a framework for understanding the distribution of fermions among quantum states.

chatGPT

Question 15

What is a “partition function?”

Answer 15

Physically, the partition function encapsulates the various ways energy can be distributed among the different quantum states of a system. It describes the total number of states available to a system at a given temperature.

It is a mathematical expression that sums up the contributions of all possible energy levels, each weighted by the Boltzmann factor, which accounts for the probability of that energy level being occupied due to the system’s temperature.

chatGPT

Question 16

An increase in the number of microstates (Ω) increases simultaneously with an increase in _____.

Answer 16

Entropy S

Boyd, NEGD, 96

Question 17

True or False
The partition function can be used to determine all the classical thermodynamic properties.

Answer 17

True.

Boyd, NEGD, 99

Question 18

The total partition function is the product of the individual partition functions of all __________.

Answer 18

Contributing energy sources.

Boyd, NEGD, 103

Question 19

For moderate temperatures (e.g., less than 3000 K), the effects of rotation and vibration are _________ than those for electronic energy states.

Answer 19

More important.

Boyd, NEGD, 107

Question 20

True or False
For moderate temperatures (300 - 5000 K), N_2, O_2, and NO behave classically with three degrees of freedom.

Answer 20

True

Boyd, NEGD, Pg. 111

Question 21

True or False
For moderate temperatures (300 - 5000 K), a parcel of molecules containing N_2, O_2, and NO the following applies:

The rotational mode behaves classically with 4 degrees of freedom.

Answer 21

False.
The rotational mode behaves classically with 2 degrees of freedom.

Boyd, NEGD, Pg. 111

Question 22

In simple terms, what does the Boltzmann distribution describe?

Answer 22

How energy states are populated at a given temperature.

Question 23

True or False
In permutations the order does not matter. In combinations, it does.

Answer 23

False.
Order matters for permutations, while for combinations, it does not.

Molecular Physical Chemistry for Engineers, Pg. 194

Question 24

What is an ensemble?

Answer 24

A collection of non-interacting systems in the same TD state.

Question 25

What is a canonical ensemble?

Answer 25

An ensemble having the same temp, pressure and composition.

Question 26

True or False
The macroscopic properties of a system are a manifestation of the time-averaged fluctuations in the quantum states of the system.

Answer 26

True

Question 27

True or False
The energy of a quantum state depends on N and V. The population of quantum states depends on T.

Answer 27

True.