Lecture 18 — The Canonical Ensemble
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Lecture 18 — The Canonical Ensemble Chapter 6, Wednesday February 20 th. Rotational energy levels in diatomic molecules Vibrational energy levels in diatomic molecules More on the equipartition theorem. Reading: All of chapter 5 (pages 91 - 123) Homework 5 due next Friday (22nd)

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Lecture 18 — The Canonical Ensemble

Chapter 6, Wednesday February 20th

  • Rotational energy levels in diatomic molecules

  • Vibrational energy levels in diatomic molecules

  • More on the equipartition theorem

Reading: All of chapter 5 (pages 91 - 123)

Homework 5 due next Friday (22nd)

Homework assignments available on web page

Assigned problems, Ch. 5: 8, 14, 16, 18, 22


Rotational energy levels for diatomic molecules

l = 0, 1, 2... is angular momentum quantum number

I = moment

of inertia

CO2 I2 HI HCl H2

qR(K) 0.56 0.053 9.4 15.3 88


Vibrational energy levels for diatomic molecules

n = 0, 1, 2... (harmonic quantum number)

w

w = natural

frequency of

vibration

I2 F2 HCl H2

qV(K) 309 1280 4300 6330


Specific heat at constant pressure for H2

CP = CV + nR

H2 boils

w

CP (J.mol-1.K-1)

Translation


More on the equipartition theorem

Classical uncertainty:

Where is the particle?

V(x)

V = ∞

V = ∞

V = 0

W = 9

x

x = L


More on the equipartition theorem

Classical uncertainty:

Where is the particle?

V(x)

V = ∞

V = ∞

V = 0

W = 18

x

x = L


More on the equipartition theorem

Classical uncertainty:

Where is the particle?

V(x)

V = ∞

V = ∞

V = 0

W = 36

x

x = L


More on the equipartition theorem

Classical uncertainty:

Where is the particle?

V(x)

V = ∞

V = ∞

V = 0

W = ∞

S = ∞

x

x = L


More on the equipartition theorem: phase space

Area h

Cell:

(x,px)

dpx

px

dx

x


More on the equipartition theorem: phase space

Area h

Cell:

(x,px)

dpx

px

dx

x


More on the equipartition theorem: phase space

Area h

Cell:

(x,px)

dpx

px

dx

x


More on the equipartition theorem: phase space

In 3D:

Uncertainty relation:

dxdpx = h

dpx

dx



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