Thermodynamics and Statistical Mechanics: Intermediate

Question 1

How to count degrees of freedom

Answer 1

The number of degrees of freedom is the number of quadratic terms in the hamiltonian

Question 2

n choose m definition

Answer 2

Question 3

Stirling’s formula for asymptotic values of ln(n!)

Answer 3

Question 4

Work done by a reversible process

Answer 4

Question 5

Entropy change for a reversible process

Answer 5

Question 6

Isentropic processes

Answer 6

An isentropic process is one with no net change in entropy. It is equivalent to a process which is reversible and adiabatic. An example is compressing a gas in a cylinder.

Question 7

Free expansion

Answer 7

When a gas suddenly expands from a smaller region to a larger region. The temperature of an ideal gas does not change during free expansion.

Question 8

Fundamental thermodynamic identity

Answer 8

Question 9

Definition of temperature

Answer 9

Question 10

Relation between derivatives of P and T

Answer 10

Question 11

Definition of heat capacity at constant X (X = V or P)

Answer 11

Question 12

Formula used for calculation of heat capacity at constant volume

Answer 12

Question 13

Relation between ideal gas heat capacities

Answer 13

Question 14

Specific heat (c)

Answer 14

Question 15

Maximum efficiency for a heat engine

Answer 15

Question 16

Work done on a PV diagram

Answer 16

In a PV diagram, the work done is just the area of the interior of the shape.

Question 17

Fermi-Dirac distribution

Answer 17

Question 18

Bose-Einstein distribution

Answer 18

Question 19

What is the mu in the Fermi-Dirac and Bose-Eintsein formulas?

Answer 19

It is the chemical potential, which is, roughly speaking, the energy associated with adding or removing a particle from the system.

Question 20

Grand canonical ensemble

Answer 20

Like the canonical ensemble, but instead of fixing the number particles, you fix the chemical potential.

Question 21

Degeneracy factors in quantum statistical mechanics

Answer 21

For discrete states, we have g(E_i), which gives the number of states with the i^th energy. If the energy levels are roungly continuous, we instead use the density of states.

Question 22

Number of particles total in the discrete energy case

Answer 22

Question 23

Number of particles total in the continuous energy case

Answer 23

Question 24

Heat capacity of an ideal relativistic gas

Answer 24

Question 25

Debye law (for low temperatures)

Answer 25

Question 26

Heat flow law

Answer 26