You are designing a system to manage the water transport in the fuel cell. A str

Question

You are designing a system to manage the water transport in the fuel cell. A stream of saturated air with a flow rate of 2.0 lit/min (humidified at 80 oC) is mixed with another stream of saturated air with a flow rate of 1.0 lit/min (humidified at 60 oC). The resulting stream is cooled to 15 oC. Calculate the fraction of water which condenses. The vapor pressure of water at 80, 60 and 15 oC are 47.36, 19.92 and 1.7 kPa, respectively. 1 atm=100 kPa. R=0.082 lit atm/molK. You are designing a system to manage the water transport in the fuel cell. A stream of saturated air with a flow rate of 2.0 lit/min (humidified at 80 oC) is mixed with another stream of saturated air with a flow rate of 1.0 lit/min (humidified at 60 oC). The resulting stream is cooled to 15 oC. Calculate the fraction of water which condenses. The vapor pressure of water at 80, 60 and 15 oC are 47.36, 19.92 and 1.7 kPa, respectively. 1 atm=100 kPa. R=0.082 lit atm/molK.

Explanation / Answer

At 80 deg.c

Partial pressure of water at 80 deg.c= vapor pressure = 47.36 Kpa

Flow rate = 2 Lt/min, P= 1atm, T= 80 deg.c= 80+273= 353 K, n= number of moles of air and water vapor = PV/RT= 1*2/(0.082*353)= .069 moles

Moles of water vapor/ total moles = partial pressure of water vapor/ total pressure = 47.36/100

Moles of water vapor /min= 0.069*= 0.032678 , moles of air/min = 0.069-0.032678= 0.0363

At 60 deg.c ( 60+273=333) , number of moles of mixture of air and water vapor = 1*1/(0.082*333)=0.0366

Moles of water vapor /min= (19.92/100)*0.0366=0.0073. moles of air/min = 0.0366-0.0073=0.0293

Total moles of dry air remain the same during cooling which = 0.0363+0.0393=0.0756 moles/min

At 15 deg.c, partial pressure of water vapor = 1.7 Kpa

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

1.7/(100-1.7)= moles of water vapor/0.0756

Moles of water vapor =0.001307 moles/min

Moles of water vapor condensed/min =total moles of water of combined stream- moles of water vapor at 15 deg.c = 0.0756-0.001307 =0.074293 moles/min

Fraction of water condensed = 0.074293/0.0756 =0.982

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