Gases Part 1

Question 1

What is needed to calculate the properties of a gas in SM?

Answer 1

Energy levels and Degeneracy
Z_i and Z_N
Functions of state

Question 2

What are the bounds of a box of side L?

Answer 2

-L/2≤x≤L/2

Question 3

What is the wavefunction of a singe particle?

Answer 3

Ψ_x=Ae^ik_xx

Question 4

What is the wavevector?

Answer 4

|k|=2π/λ

Question 5

What is the boundary condition for a particle in a box?

Answer 5

Ψ_x(-L/2)=Ψ_x(L/2)

Question 6

What is the volume occupied by one k-state?

Answer 6

2π/L * 2π/L * 2π/L

Question 7

What is the density of states?

Answer 7

Number of allowed states with vector of magnitude between k and k+dk

Question 8

What is the value of the density of states in 3D?

Answer 8

g(k)dk=VK²/2π² dk

Question 9

What is the new single particle partition function?

Answer 9

Z₁=∫e^-βE(k)g(k)dk
From 0 to infinity

Question 10

What is the equation for momentum?

Answer 10

p=ℏk

Question 11

What is the energy of a photon?

Answer 11

E=ℏ²k²/2m(=p²/2m)

Question 12

What is the equation for quantum concentration?

Answer 12

n_Q=(mk_BT/2πℏ²)^3/2

Question 13

What is the equation for thermal wavelength?

Answer 13

λ_th=h/sqrt(2πmk_BT)

Question 14

What is the thermal wavelength?

Answer 14

The de Broglie wavelength of a particle at temperature T

Question 15

What does the thermal wavelength represent?

Answer 15

The characteristic size of the particle’s wavefundtion

Question 16

What is the quantum concentration?

Answer 16

The concentration at which particles are separated by λ_th

Question 17

How do the quantum concertation and thermal wavelength relate?

Answer 17

n_Q=1/λ³_th

Question 18

What happens if n«n_Q?

Answer 18

No wavefunction overlap
Classical gas

Question 19

What happens if n»n_Q?

Answer 19

Wavefunctions overlap
Quantum gas