At the back of this book is a table of thermodynamic data for selected substances at room temperature. Browse through the $C_P$values in this table, and check that you can account for most of them (approximately) using the equipartition theorem. Which values seem anomalous?

Table of thermodynamic data for selected substances at room temperature.

$C_P=8.31\left(1+\frac{3}{2}\right)$

For an ideal gas at constant pressure

$C_P=nR\left(1+\frac{f}{2}\right)$

In SI units, $R=8.31.\mathrm{J}·{\mathrm{mol}}^{-1}·{\mathrm{K}}^{-1}$. So for one mole for an ideal gas:

$C_p=8.31\left(1+\frac{f}{2}\right)$

Because we have three transitional degrees of freedom in monatomic gases, f=3, the heat capacity of monatomic gases is:

$C_P=8.31\left(1+\frac{3}{2}\right)$

$C_P=20.775\mathrm{J}·{\mathrm{C}}^{-1}$

This is in great agreement with the monatomic gases hydrogen, argon, helium, and neon, according to the table in Schroeder's book's appendix.

We have three transitional degrees of freedom and two rotational degrees of freedom in diatomic gases (f=5). As a result, the heat capacity of diatomic gases is:

$C_P=8.31\left(1+\frac{6}{2}\right)$

$C_P=33.24\mathrm{J}·{\mathrm{C}}^{-1}$

which is quite close to the values for ${\mathrm{O}}_2,{\mathrm{N}}_2$and ${\mathrm{H}}_2$and $CO$but the heat capacity of ${\mathrm{Cl}}_2$is higher than this value.

With three transitional degrees of freedom, two rotational degrees of freedom, and one vibrational degree of freedom in a polyatomic molecule, f=0, the heat capacity of diatomic gases is:

$C_P=8.31\left(1+\frac{6}{2}\right)$

$C_P=33.24\mathrm{J}·{\mathrm{C}}^{-1}$

From the table, the heat capacity for carbon dioxide is $C_P=33.24\mathrm{J}·{\mathrm{C}}^{-1}$which is higher than $C_P=33.24\mathrm{J}·{\mathrm{C}}^{-1}$by 3.87

For most solids and liquids, the heat capacity at constant pressure is given by:

$C_P\approx 8.31\frac{f}{2}$

much then f=0 the heat capacity is therefore:

$C_P=8.31\frac{6}{2}$

$C_P=24.93\mathrm{J}·{\mathrm{C}}^{-1}$