@Loong may I ask the motivation behind: "You should also not rely on chemical catalogues (e.g. Sigma-Aldrich) or online databases (e.g. ChemSpider)."? (src)
do you intend to convey that they often generate incorrect names?
Yes, such sources sometimes tend to use the traditional names that have been frequently used in the past (e.g. in literature) but don't necessarily promptly follow the changes in IUPAC recommendations or are not updated at all. Thus, if you want to be sure that a name is in accordance with the current nomenclature recommendations, better don't rely on such sources. However, the names are not necessarily incorrect.
For an ideal gas, we have
$$C_p - C_V = nR$$
where
$C_p$ is heat capacity at constant pressure,
$C_V$ is heat capacity at constant volume,
$n$ is amount of substance, and
$R=8.3144598(48)\ \mathrm{J\ mol^{-1}\ K^{-1}}$[source] is the molar gas constant.
How can I prove this?
From what I've read, my impression is that with a sufficient number of scans etc., one can get spectra from even very dilute samples (S:N ratio ~ $\sqrt{\text{NS}}$). Obviously, this is not always possible in practice and it is not necessarily efficient use of instrument time.
However, assuming ...