Question

Air at 38.0°C and 99.0% relative humidity is to be cooled to 16.0°C and fed into a plant area at a rate of 510.0 m³/min. You may assume that the air pressure is 1 atm in all stages of the process.

Calculate the rate the water condenses in kg/min.

Answer 1

at 38 deg.c, vapor pressure of water = 49.7 mm Hg

relative humidity = 100*(partial pressure of water vapor/ vapor pressure of liquid)

partial pressure of water vapor/vapor pressure of liquid =0.99

parital pressure of water vapor = 0.99*49.7 =49.2 mm Hg

Flow rate of wet air = 510 m3/min=510*1000 L/min ( 1m3= 1000L)

Moles of wet air can be calculated from ideal gas,

n= number of moles of wet air ( dry air+ water vapor)= PV/RT= 1*510*1000 /{0.0821*(38+273.15)} =19964.44 moles/min

Partial pressure of water vapor/ partial pressure of dry air =

(moles fraction of water vapor * total pressure/ ( mole fraction of ary t air* total pressure )

mole fraction of water vapor/ mole fraction of dry air

moles of water vapor/ moles of dry air

hence partial pressure of water vapor/ partial pressure of dry air= moles of water vapor/ moles of dry air

49.2/(760-49.2)= moles of water vapor/ moles of dry air

mole of water vapor = 0.0692* mole of dry air

Mole of water vapor + mole of dry air = 19964,44

0.0692* moles of dry air+ moles of dry air = 19964.44

Mole of dry air = 19964.44/1.0692=18282.46 moles/min

Moles of water vapor= 19964.44-18282.46 =1682 moles/min

when cooled to 16 deg.c, dry air moles remain the same and only water vapor condenes

Also at 16 deg.c, the air is expected to be saturated wtih water vapor. i.e partial pressure of water vapor= Vapor pressure of liquid

at 16 deg.c, vapor pressure of liquid = 13.6 mm Hg

partial pressure of water vapor = 13.6 mmm Hg

at 16 deg.c, partial pressure of water vapor/ partial pressure of dry air = moles of water vapor/ moles of dry air

partial pressure of water vapor/ partial pressure of dry air = moles of water vapor /moles of dry air

13.6/(760-13.6)= moles of water vapor/18282.46

moles of water vapor= 333.12 moles/min

moles of water condensed= moles of water vapor at 38 deg.c- moles of water vapor at 16 deg.c= 1682- 333.12 =1348.88 moles/min