Thermo-D Problem I'm Stuck On

I am studying for the CA Mechanical FE. Tragically, I'm stuck on a Thermo problem. Can anyone help? I've attached my work up to the point where I'm stuck, and the problem statement is below. My situation is that I have no info for the final state except the relative humidity, and know of no way to resolve the unknowns so that I can solve for omega2 which will lead to the part a) answer. For the unknowns see my last line equation, all subscripts containing '2'. Also, h sub f, which is the enthalpy of the moisture coming off of the clothes is unknown, as well as T sub f, which is temperature thereof. Any tips would be greatly appreciated. Thanks!

THE PROBLEM:

Air enters a drier at 120℉, 14.7 psia, and 10% relative humidity. It leaves the drier at 14.7 psia and a relative humidity of 90%. For an airflow rate of 5000 lbm/hr, determine a) The amount of moisture picked up by the air in lbm/hr. b) The dry bulb temperature of the air at drier outlet.

Fellow scientists, regarding my recent post I now realize that I hadn't properly understood the problem. The 120℉ air entering the drier is apparently after pre-heating, which was not how I understood out. So the work I've shown is not precisely on the right track, especially the process path on the T-S diagram. The exit temperature is lower than 120℉, not higher.

Still though, I'm stuck on the unknowns of the final state and could use any tips. Sorry for the bad start!

I think I figured it out. It's an adiabatic saturation process so h2 ~ h1. So omega2 can be gotten from the psychometric chart. I will visit that ASAP to hopefully confirm it works.

psychrometric

It seems to work. My part b) answer is 2.5% off from the books answer. Not completely sure why, but I'm pretty sure that the psychrometric chart is the expected method.

Based on the above, it appears you haven't recopied the precise problem. I say this because you noted "The 120℉ air entering the drier is apparently after pre-heating" when the problem you posted does not include that detail, but I fail to see how that affects the starting point of the problem solution process.  Is the given 120 deg. F air a dry bulb temperature?  Assuming that it is, from the psychrometric chart you get a humidity ratio of about .0071 with no more practical accuracy than that, at that point.  So, if you're using your calculated value for that and also for your other values that could be gleaned from the chart, that is likely where the 2.5% comes in to play.  I'd be curious to see what the published answers are.