Heat Capacity from Spectroscopic Data

KQueeney's Values

From Infrared  (IR) spectroscopy  K. Queeney '92 found the following fundamental frequencies of the three normal modes of [Graphics:../Images/MATH.LAB.CHEM155.ST_gr_45.gif]

[Graphics:../Images/MATH.LAB.CHEM155.ST_gr_46.gif]

Some parameters

[Graphics:../Images/MATH.LAB.CHEM155.ST_gr_47.gif]

We define the following function of temperature

[Graphics:../Images/MATH.LAB.CHEM155.ST_gr_48.gif]

From Statistical Mechanics we know that the contribution to the heat capacity due to the vibrational modes is given by:

[Graphics:../Images/MATH.LAB.CHEM155.ST_gr_49.gif]

Now, the heat capacity at two different temperatures

[Graphics:../Images/MATH.LAB.CHEM155.ST_gr_50.gif]
[Graphics:../Images/MATH.LAB.CHEM155.ST_gr_51.gif]

For sulfur dioxide the total heat capacity is given by:

[Graphics:../Images/MATH.LAB.CHEM155.ST_gr_52.gif]

Finally the heat capacity at two different temperatures is

[Graphics:../Images/MATH.LAB.CHEM155.ST_gr_53.gif]
[Graphics:../Images/MATH.LAB.CHEM155.ST_gr_54.gif]

Problem 2. - Plot the specific heat from 10 K to 2000 K.


Converted by Mathematica      October 2, 2002