Kappa, Isentropic Exponent for Real Gas, for Moist Air

I would suggest a way to estimate it:

at 35°C the air density is 1.13 kg/m^3 Cp= 1007 J/kgK and Cv= Cp/1.4= 719.3 J/kgK

water content will be at 100% RH 702.9 g/m^3 and at 80% 562 g/m^3=0.592 kg/m^3

water vapor has at same temp Cp=1914 J/kgK and Cv= Cp /1.33 =1439.1 J/kgK

1.33 being the ration for water vapor around 20°C according to a table I did not try to interpolate

The total mass of 1m^3 of mixture = 1.13+0.562= 1.692 kg

Thus Cpmix= (Cpair*Mair+Cpvapor*Mvapor)/Mmixt= 1308 j/kgK

Cvmix= 958.4 J/kgK >>>> Cpmix/Cvmix= 1.365

The equation is logically correct since all is related to MASS which is an invariant.

Since 1.365 is near to 1.4 the "error" is not big if 1.4 is used, it is within normal technical uncertainty range.

This way it is very simple to have a result and it seems to be OK.

Hi nick

I see what you've done and thanks for this, I'm going to give it a go in work tomorrow and see how it compares to a paper on it I've bought.

The paper provided a formula (determined from RH and temp) which gave specific heat ratio kappa (or gamma) = 1.3966

The only little thing in your calcs is you've not taken into account mole fraction of the mixture and therefore your density is too high for the mixture. At 80%RH and 35°C (and mean sea level) density is 1.126 kg/m3; as moist air is less dense that dry air.

Easy enough to add into your calc though. I'll see how it works out.

Thanks again.

I agree it was a "quick" attempt and I neglected some aspects in order to do it fast.

After correction the value is 1.3955. The difference is in the water quantity/m^3 of mixture. the new value justifies even more the use of k=1.4