Nick,

I could trot out the whole handwaving discussion about energy modes, partition functions, classical statistical mechanics versus quantum mechanics, etc. (but I won't).

Here are the raw numbers:

Air [mole fractions]
N2 0.7812
O2 0.2095
Ar 0.0093
Pressure 1 atm
Temperature 20 deg.C
Density 1.2039 kg/m^3
Molecular Weight 28.959
Cp 1.0046e3 joules/(kg deg.K)
29092.2114 joules/(moles deg.K)
Ratio of specific heats 1.4001
Speed of Sound 343.3 m/sec

Jupiter Atmosphere [mole fractions]
H2 0.86229
CH4 0.00181
He 0.13590
Pressure 1 atm
Temperature 20 deg.C
Density 9.6081-2 kg/m^3
Molecular Weight 2.311
Cp 11.9948e3 joules/(kg deg.K)
27719.9828 joules/(moles deg.K)
Ratio of specific heats 1.4284
Speed of Sound 1227.3 m/sec

The quantity "Cp" is specific heat at constant pressure. When people talk about "heat capacity" for a gas they are usually talking about Cp. Notice that Cp when cast as "joules/(moles deg.K)" is not too different between Jupiter's atmosphere and air (this quantity at this temperature is driven mainly by molecular translational energy). However there is an order-of-magnitude difference if Cp is cast as joules/(kg deg.K). The thing that drives aerodynamics and convective heat flux is free stream density and velocity. Therefore the relevant Cp is joules/(kg deg.K). The reason why Jupiter's atmosphere has so much heat capacity is because it has such a low molecular weight (more molecules bouncing around for a given density).

Gary