Statistical Mechanics Flashcards
What is the goal of statistical mechanics?
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
Define the degree of molecular randomness.
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
What is a “microstate?”
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
Particles that have an even number of elementary units are called ______.
Bosons.
Boyd NEGD, Pg 85
True or False
Bosons are analyzed using Bose-Einstein statistics.
True.
Boyd NEGD, Pg 85
Give some examples of Bosons.
Hydrogen atoms
He^4
N_2
Photons
Boyd NEGD, Pg 85
Particles made up of an odd number of elementary particles are called ______.
Fermions.
Boyd NEGD, Pg 85
True or False
Fermions are analyzed using Bose-Einstein statistics.
False. They are analyzed using Fermi-Dirac statistics.
Boyd NEGD, Pg 85
True or False
No two Fermions can occupy the same state.
True.
Boyd NEGD, Pg 85
What are some examples of Fermions?
- Electrons, protons, and He^3
Boyd NEGD, Pg 85
True or False
For Bosons, there is no limit on the number of particles in each energy state.
True.
Boyd NEGD, Pg 88
True or False
Bosons follow the Pauli exclusion principle.
False. Fermions follow this principle.
Wikapedia
Give the general purpose of Bose-Einstein statistics.
Bose-Einstein statistics describe the statistical distribution of indistinguishable particles called bosons that can occupy the same quantum state.
chatGPT
What is the general purpose of Fermi-Dirac statistics?
The purpose of Fermi-Dirac statistics in statistical mechanics is to provide a framework for understanding the distribution of fermions among quantum states.
chatGPT
What is a “partition function?”
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
An increase in the number of microstates (Ω) increases simultaneously with an increase in _____.
Entropy S
Boyd, NEGD, 96
True or False
The partition function can be used to determine all the classical thermodynamic properties.
True.
Boyd, NEGD, 99
The total partition function is the product of the individual partition functions of all __________.
Contributing energy sources.
Boyd, NEGD, 103
For moderate temperatures (e.g., less than 3000 K), the effects of rotation and vibration are _________ than those for electronic energy states.
More important.
Boyd, NEGD, 107
True or False
For moderate temperatures (300 - 5000 K), N_2, O_2, and NO behave classically with three degrees of freedom.
True
Boyd, NEGD, Pg. 111
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.
False.
The rotational mode behaves classically with 2 degrees of freedom.
Boyd, NEGD, Pg. 111
In simple terms, what does the Boltzmann distribution describe?
How energy states are populated at a given temperature.
True or False
In permutations the order does not matter. In combinations, it does.
False.
Order matters for permutations, while for combinations, it does not.
Molecular Physical Chemistry for Engineers, Pg. 194
What is an ensemble?
A collection of non-interacting systems in the same TD state.
What is a canonical ensemble?
An ensemble having the same temp, pressure and composition.
True or False
The macroscopic properties of a system are a manifestation of the time-averaged fluctuations in the quantum states of the system.
True
True or False
The energy of a quantum state depends on N and V. The population of quantum states depends on T.
True.
