Vibrational temperature: Difference between revisions

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The vibrational temperature is commonly used in thermodynamics, to simplify certain equations. It has units of temperature and is defined as

\theta _{\text{vib}}={\frac {h{\tilde {\nu }}c}{k_{\text{B}}}}={\frac {h\nu }{k_{\text{B}}}}

where $k_{\text{B}}$ is the Boltzmann constant, $c$ is the speed of light, and $\nu$ (Greek letter nu) is the characteristic frequency of the oscillator.

The vibrational temperature is used commonly when finding the vibrational partition function.

Molecule	${\tilde {v}}$	$\theta _{vib}$
N₂	2446 cm⁻¹	3521 K
O₂	1568 cm⁻¹	2256 K
F₂	917 cm⁻¹	1320 K
HF	4138 cm⁻¹	5957 K
HCl	2991 cm⁻¹	4303 K

References

Statistical thermodynamics University Arizona

@@ Line 1: / Line 1: @@
 The '''vibrational temperature''' is commonly used in [[thermodynamics]], to simplify certain equations. It has units of [[temperature]] and is defined as
+: <math>\theta_\text{vib}= \frac {h \tilde{\nu} c}{k_\text{B}} = \frac{h\nu}{k_\text{B}}</math>
+where <math>k_\text{B}</math> is the [[Boltzmann constant]], <math>c</math> is the [[speed of light]], and <math>\nu</math> (Greek letter nu) is the characteristic frequency of the oscillator.
-<math>\theta _{vib}= \frac {h\nu}{k_{B}}</math><br />
-where <math>k_B</math> is [[Boltzmann's constant]]
 The vibrational temperature is used commonly when finding the [[vibrational partition function]].
 {| class="wikitable sortable"
 |-
-! Molecule !! <math><tilde>{v}</math>  !! θ<sub>vib</sub>
+! Molecule !! <math>\tilde{v}</math> !!  <math>\theta_{vib}</math>
 |-
-| N<sub>2</sub> || Example || Example
+| N<sub>2</sub> || 2446&nbsp;cm<sup>−1</sup> || 3521&nbsp;K
 |-
-| O<sub>2</sub> || Example || Example
+| O<sub>2</sub> || 1568&nbsp;cm<sup>−1</sup> || 2256&nbsp;K
 |-
-| F<sub>2</sub> || Example || Example
+| F<sub>2</sub> || 917&nbsp;cm<sup>−1</sup> || 1320&nbsp;K
 |-
-| HF || Example || Example
+| HF || 4138&nbsp;cm<sup>−1</sup> || 5957&nbsp;K
 |-
-| HCl || Example || Example
+| HCl || 2991&nbsp;cm<sup>−1</sup> || 4303&nbsp;K
 |}
-==References==
-[http://www.chem.arizona.edu/~salzmanr/480b/statt02/statt02.html/ Statistical thermodynamics University Arizona]
-==See also==
+== References ==
+* [https://web.archive.org/web/20010415024929/http://www.chem.arizona.edu/~salzmanr/480b/statt02/statt02.html Statistical thermodynamics University Arizona]
-*[[Rotational temperature]]
-*[[Rotational spectroscopy]]
+== See also ==
-*[[Vibrational spectroscopy]]
-*[[Infrared spectroscopy]]
+* [[Rotational temperature]]
+* [[Rotational spectroscopy]]
-*[[Spectroscopy]]
+* [[Vibrational spectroscopy]]
+* [[Infrared spectroscopy]]
+* [[Spectroscopy]]
 [[Category:Atomic physics]]
 [[Category:Molecular physics]]
+{{Molecular-physics-stub}}
+{{thermodynamics-stub}}