Partition functions and properties of ideal gases

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Partition functions and properties of ideal gases

• 9/15/03

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Our main conclusion from last class

• If the of available quantum states is gtgt N, we
  can write Q(N,V, T)

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Monoatomic ideal gas
eatomic etrans eelec q(v,T) qtrans (V,T)
qelec(T)
Sum over levels
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The electronic molecular partition function
Because we define that the ground state has
energy zero.
For most atoms at ordinary Ts, only the first
term counts. (see Table 4.1) kBT 0.695
cm-1/K(298K)207 cm-1
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Properties of the monoatomic ideal gas

• u ltegt (3/2)RT for one mole of a monoatomic
  ideal gas (because the second term contribution
  is negligible)
• cv 3/2 R
• P (NkBT)/V

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Properties of the diatomic ideal gas
eatomic etrans erot evib eelec q(v,T)
qtrans qrot qvib qelec qtrans is similar to
that for one atom
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Electronic contribution for a diatomic
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Vibrational pf for a diatomic
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Vibrational temperature
What is the limit of cv,vib at high T
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Cv,vib ideal diatomic gas
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Fig. 4.4 (population of vibrational levels of Br2
(g) at 300 K
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Rotational states of a diatomic
Rigid rotator
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Rotational temperature
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Rotational energy of a diatomic
Two rotational degrees of freedom, each
contributes R/2 to the cv,rot
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Fig. 4.5 fraction of molecules in the Jth
rotational level for CO at 300K
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Symmetry number

• s is the number of indistinguishable orientations
  of the molecule
• Only if the diatomic is heteronuclear such as CO,

s 2 for a homonuclear
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Finally, for the ideal gas diatomic
ZPE
Elect. energy
3 transl. DoF
Vib. Energy at finite T
2 rot. DoF
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Polyatomic molecule
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Vibrational motion set of independent harmonic
oscillators
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Normal modes are independent
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See example 4-6
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Fig. 4.6 Contribution of each normal mode to
cv,vib for CO2
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Rotational pf for a polyatomic

• Case of a linear polyatomic

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Rotational temperature (nonlinear polyatomic)
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Properties of a nonlinear polyatomic
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Fig. 4.7 Molar cv,vib/R of water vapor (calc.
and exp.)