I found the definitive answer to my question here:
http://www.not2fast.com/turbo/glossary/turbo_glossary.shtml#compressor_efficiency "Compressor Efficiency (Turbocharger Efficiency)
Compressor efficiency is a measure of how well the compressor wheel uses its kinetic energy to compress air (the remainder of the energy is turned into heat in the compressed charge). In an ideal system, compression of the input fluid would raises its temperature adiabatically. This is never the case in the real world, so all calculations must take the compressor efficiency into account.
In order to calculate compressor outlet temperature, you must know compressor efficiency, pressure ratio and ambient temperature.
(PR^0.283 - 1) * Tambient
Trise = ---------------------------
Ec
Trise = increase in temperature
PR = pressure ratio
Tambient = ambient temperature (in an absolute scale, Kelvin or Rankine)
Ec = Efficiency of the compressor
The exponent of the pressure ratio arises from the molecular structure of the gas. Diatomic gasses (like N2 and O2) have seven degrees of freedom, five of which are excitable at STP. Thus gamma = 7/5 in the equation P(V^gamma) = constant, and we can derive an exponent of 1 - (1/gamma) = 0.285. For real air, containing non-diatomic molecules like CO2, a better value is 0.283.
For more on this, see the gas thermodynamics section of Nuclear Weapons FAQ (!) (scan down to section 3.1.6).
So, for example, my Garrett T04E compressor running at PR of 2.5, Ec of 0.75 in the good old summer time with a temperature of 27 degrees Celsius (300 Kelvin) produces:
(2.5^0.283 - 1) 300
Trise = ---------------------
0.75
= 118°"
So now you now where ^.283 came from. There are probably a couple of you on here that understand all of that. By the way, you can find the root .250 of any number on a common calculator because this is actually the square root of the square root of the number. I found that by doing this using the number 2 as the pressure ratio, that taking the sq. rt. of the sq. rt. gave me an answer within 4% of using the computer to find the .283 root. In case you want to do the math and don't happen to have access to the net, like on the Salt Flats. Assuming, of course, that you have all the other information and formulas at hand.
