quark:
"Gas SG can't be the ratio of gas density at actual conditions to air density at standard condition. In that case gas SG closely follows its actual density as the air density at standard conditions is about 1.2 bar."
I am assuming you meant 1.2 kg/m³, and not 1.2 bars for the density of air at standard conditions. Also, please note that I asked for USC units, and not SCI units.
"Did some calculations for 10 gases at pressures ranging from 0 to 100 bar g (more or less close to ideal conditions) and SG values by pressue definition (i.e actual gas density/air density at gas conditions) differ after second decimal when compared with SG values by molecular weight definition."
I ran my own numbers and found a much bigger difference than the second decimal place as you described. Here are my sample calculations, using steam as the example fluids.
Using MW to define SG:
Steam MW: 18.02
Air MW: 28.966
SG = 18.02/28.966 = 0.622
Using density to define SG:
Steam density @ 114.7 psia/400 °F = 0.2338 lb/ft³
Air density @ standard conditions = 0.075 lb/ft³
SG = 0.2338/0.075 = 3.12
As you can see, there is quite a bit of difference between the two values. Just for fun, I wanted to see what the SG of steam at 14.7 psia would be:
Using density to define SG:
Steam density @ 14.7 psia/212 °F = 0.0373 lb/ft³
Air density @ standard conditions = 0.075 lb/ft³
SG = 0.0373/0.075 = 0.497
As you can see, there is a big difference in SG when the vapor is under pressure.
I spoke to a mechanical engineer here, and he stated that the MW version, that everyone on this forum keeps referencing, is only valid for ideal gases.