lab Assignment
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maxwell-boltzmann_presentationA.pdf
Maxwell-Boltzmann Distributions
• How do we describe the energy of a whole bunch of par6cles?
• More useful to describe the energy of a system of par6cles
Energy Equipartition
Each degree of freedom contributes to the energy of a system, where possible degrees of freedom are those associated with transla6on, rota6on, and vibra6on of molecules.
Energy Equipartition: Monatomic gas
(made of single atoms)
3 Dimensions, so 3 transla6onal degrees of freedom 𝐸= 3/2 𝑘↓𝐵 𝑇
Kinetic Energy 𝐾= 1/2 𝑚𝑣↑2
Par6cles of different masses and veloci6es will have different energies
Relate velocity and temperature • For an ideal monatomic gas
𝐸=𝐾
3/2 𝑘↓𝐵 𝑇= 1/2 𝑚𝑣↑2
𝑣↓𝑟𝑚𝑠 =√3𝑘↓𝑏 𝑇/𝑚
So let’s take a look at a system of particles with different masses
hEps://phet.colorado.edu/sims/html/gas-‐proper6es/latest/gas-‐proper6es_en.html
2 0 B
3/2 /220
B
4 2
m v k T v
m N N v e
k T π
π −⎛ ⎞= ⎜ ⎟
⎝ ⎠
Figure 20.10
Equa6on 20.42
Maxwell Boltzmann Distribution
𝑣↓𝑚𝑝 = most probable velocity 𝑣↓𝑎𝑣𝑔 = average velocity 𝑣↓𝑟𝑚𝑠 = root-‐mean-‐square velocity
How would the MB distribution change with T?
Figure 20.11
2 0 B
3/2 /220
B
4 2
m v k T v
m N N v e
k T π
π −⎛ ⎞= ⎜ ⎟
⎝ ⎠
Figure 20.11
