SPECIFIC VOLUME VS. SPECIFIC VOLUME

You may have noticed the table of 'Psychrometric Chart Properties' displayed on this page includes a value called 'moist air specific volume'.  Similarly, the table of 'Other Thermodynamic Properties' includes a value of specific volume, and the values are different!  So what gives?

As we all know, specific volume is the ratio of the volume occupied by the sample in question to the total mass of that sample. In the present case, the sample is question is moist air.  Density, of course, is the reciprocal of specific volume.

However, [moist air] specific volume, as defined in ASHRAE STD 41.6 (and reiterated in Chapter 6 of the HOF), is expressed in terms of unit mass of dry air.  Mathematically, all of this can be defined as follows:

ρ = ( ma + mw)/ V
ν = 1 / ρ
νp = V / ma
   = V / ( 28.9645 Na)
   = Ra T ( p - pw)
 
Where:
ρ = density
ν = specific volume
νp = moist air specific volume
V = volume of sample
ma = mass of dry air
mw = mass of water vapor
Na = Number of moles of dry air
T  = temperature in Rankine
p  = barometric pressure
pw = partial pressure of water vapor in air sample

In the above, take note of the units of thermodynamic specific volume and moist air specific volume. The mass unit is different. The unit of mass for the former is lbm of moist air sample and for the later, lbm of dry air. For this reason, there are two things of which one must be aware. First, 'moist air specific volume' is not really a specific volume, at least not in the classic sense. It is the ratio of the total volume of the moist air sample to the mass of dry air contained within the sample. Nothing more. Second, the reciprocal of this value of specific volume does not result in density. Density is still conventionally defined as the ratio of the TOTAL mass of the air sample (i.e.: dry air plus water vapor) to the volume occupied by that sample. As such, it is the reciprocal of the 'Specific Volume' displayed in the table of 'Other Thermodynamic Properties'.

So which one should you use? All HVAC calculations, where specific volume is a variable, were derived based on the definition of specific volume referenced to a unit mass of dry air. Hence, you should always use this value, which is the value found on a typical psychrometric chart, when doing such calculations. The true value of specific volume should be used when doing more 'traditional' (for lack of a better term) thermodynamic calculations where the specific volume referenced is the reciprocal of density.