# Calculate the amount of water vapor

dbag123
Homework Statement:
Calculate the amount of water vapor when 4m^3/min or 25C air is cooled to 20C. How much vapor is condensed to water in 1 hour and how much of the vapor is still in the system.
Relevant Equations:
pV/T=c
Hello
4m3/min is 240m3 /hr. Temperature is 293K, at 25C the amount of water is 22.8g/m3 and at 20C it is 17.1g/m3. Relative humidity is 70% and absolute pressure 9bar.

Solution:
@ 25C
relative humidity lowers the water content from 22.8 to 15,96g/m3 so in total 3830.4g/hr
240m3 or air is compressed to 1/9, so 26,67m3 and in that compressed air the amount of water vapor would be 608,08 g every hour
total amount of water 3830,4g/hr, in vapor its 608,08g and in solid water 3232,3g/hr

@20C
17,1g/m3 to 11,97g/m3 due to relative humidity. total amount of water is 2872.8g
then volume is compressed to 26.67m3 actually there is in compressed air 107.73g/m3 so the amount of vapor in compressed air would be 17.1g/m3*26.67m3 or 455.9g. and in form of water 2416.9g

How does this tell me the amount of water condensed or how much of the vapor is in form of liquid water during 1 hour from temperature of 25C to 20C?

Mentor
Is that 4m^3/min at 9 bars?

dbag123
Is that 4m^3/min at 9 bars?
the problem statement does not say that. i am assuming it is 4m^3/min at 1 atm

i have left some detail out sorry about that. the air is compressed to 9bar absolute due to the cooling

Last edited:
Mentor
the problem statement does not say that. i am assuming it is 4m^3/min at 1 atm

i have left some detail out sorry about that. the air is compressed to 9bar absolute due to the cooling
This is not correct. You have moist air flowing at 9 bars, and the pressure does not change in the cooler. You have the correct water vapor density of 16.0 gm/m^3, so just multiply that by the volume flow rate of air. This will be the mass flow rate of water vapor entering. If there is any condensation at all, then the air coming out the cooler will be saturated with water vapor at 20 C. What would the gm/m^3 of water vapor be at the exit. Since the air cools from 298 to 293 K, its density increase and its volume flow rate has decreases by the exit. What would be the volume flow rate of air at the exit? What would be the gas flow rate of water vapor exiting the cooler, assuming the exit air was saturated?