20 Appendix: Thermodynamics

The thermodynamical calculations performed by VIEWMOL are using the following formulas:

Enthalphy
- Translation $H^T = \frac{3}{2}RT$
- pV (molecule)
- pV (solid)
- Rotation (linear molecule)
- Rotation (non-linear molecule) $H^R = \frac{3}{2}RT$
- Vibration
  
  $\begin{displaymath} H^V = N_A\left[\sum_i \frac{h c \bar{\nu}_i}{2} + \sum_i\fra... ...(-h c \bar{\nu}_i/k_BT)}{1-\exp(-h c \bar{\nu}_i/k_BT)}\right] \end{displaymath}$ (1)
Entropy
- Translation
  
  $\begin{displaymath} S^T = \frac{5}{2}R + R \ln\left(\frac{k_B T}{p}\left(\frac{2\pi M k_B T}{N_A h^2}\right)^{3/2}\right) \end{displaymath}$ (2)
- Rotation (linear molecule)
  
  $\begin{displaymath} S^R = R\left[1 + \ln \left(\frac{k_B T}{\sigma h A}\right)\right] \end{displaymath}$ (3)
- Rotation (non-linear molecule)
  
  $\begin{displaymath} S^R = \frac{R}{2}\left[3 + \ln \left(\frac{\pi}{\sigma}\left(\frac{k_B T}{hc}\right)^3 \frac{1}{A B C}\right)\right] \end{displaymath}$ (4)
- Vibration
  
  $\begin{displaymath} S^V = R \sum_i \left(\frac{h c \bar{\nu}_i}{k_B T}\frac{\exp... ...-\exp\left(-\frac{h c \bar{\nu}_i}{k_B T}\right)\right)\right) \end{displaymath}$ (5)
Heat capacity
- Translation $C_v^T = \frac{5}{2}R$
- Rotation (linear molecule)
- Rotation (non-linear molecule) $C_v^R = \frac{3}{2}R$
- Vibration
  
  $\begin{displaymath} C_v^V = R \sum_i \left(\frac{h c \bar{\nu}_i}{k_B T}\right)^... ...t)}{\left(1-\exp \left(-h c \bar{\nu}_i/k_B T\right)\right)^2} \end{displaymath}$ (6)

gas constant,

temperature,

pressure,

volume,

Avogadro's number,

Planck's number,

speed of light, $\bar{\nu}_i$ wave number,

Boltzmann's number,

molecular mass,

,

, and

rotational constants, $\sigma$ symmetry number. Only wave numbers which are larger than 10 cm^-1 are included.

Jörg-Rüdiger Hill Fri Oct 31 14:19:21 CET 2003