The gas constant for dry air is 278.058Jkg-1K-1 according to wikipedia.org and I verified it using S.I. units and they cancelled down to equal kg/m3.
Equations 3 and 4 seem a little odd to me. Shouldn't equation 3 have MP/RT on the right hand side, M being the molar mass in kg/mol? (The correct value to use would be the average molar mass of air, which is about 0.8 x 0.028 + 0.2 x 0.032.) Also, I'm not sure where the 287.058 comes from in the denominator of equation 4. I have fixed a couple of typographical things. Apart from the above comments, it looks very nice!