Example Problem with Complete Solution

2D-7 : Humid Air and Relative Humidity
6 pts
Humid air at 75oC, 110 kPa and 30% relative humidity is fed into a furnace at a flow rate of 1000 m3/h.  Determine the flow rate of bone dry air (BDA) into the furnace in mole/h.  Also, determine the flow rate of water (within the humid air) into the process in mole/h. Use the steam tables if necessary.
                   
Read: The two keys to this problem is that the humid air behaves as an ideal gas and the definition of relative humidity.  You can determine the mole fraction of water in humid air from the relative humidity.  You can use the Ideal Gas EOS to determine the total molar flow rate from the volumetric flow rate.  The product of the mole fraction of water and the total molar flow rate is the molar flow rate of water.  Finally, the molar flow rate of BDA is just the difference between the total molar flow rate and molar flow rate of water.
Given: T
75
°C Find : nH2O
???
mol H2O/h
P
110
kPa nBDA
???
mol BDA/h
hR
30%
Vdot
1000
m3/h
Diagram: None for this problem.
Assumptions : 1 - Humid air behaves as an ideal gas.  This allows us to use the ideal gas EOS and tells us that the partial pressure is equal to the product of the mole fraction and the total pressure.
Equations / Data / Solve :
The molar flow rates of BDA and water are related to the total molar flow rate of humid air by the mole fractions.  The equations are :
Equation. Eqn 1   Equation. Eqn 2
Because humid air is made up of bone dry air (BDA) and water, only : Equation. Eqn 3
Solve Eqn 3 for yBDA .   Equation. Eqn 4
So, we need to determine ntotal and yH2O before we can use Eqns 1, 2 & 4 to answer this question.
Let's begin by evaluating the total molar flow rate.
For this, we can use the rate version of the ideal gas EOS: Equation. Eqn 5
Solve Eqn 5 for the total molar flow rate. Equation. Eqn 6
R
8.314
J/mol-K ntotal
38003
mol total/h
The key to solving this problem is using the definition of relative humidity to determine the mole fraction of water in the humid air..
Equation. Eqn 7
We can now solve Eqn 7 for the mole fraction of water in the humid air. Equation. Eqn 8
We can look up the vapor pressure of water at 75oC in the Saturated Temperature Table of the Steam Tables.
P*H2O
38.595
kPa
Now, plug values back into Eqn 8 : yH2O
0.1053
mol H2O/mol
Finally, plug values into Eqns 1, 4 & 2 : nH2O
4000
mol H2O/h
yBDA
0.8947
mol BDA/mol
nBDA
34003
mol BDA/h
Verify : The ideal gas assumption needs to be verified.
We need to determine the specific volume and check if : Equation.
Equation. Eqn 9
V
26.31
L/mol The ideal gas assumption is valid because V > 5 L/mole.
Answers : nH2O
4000
mol H2O/h nBDA
34000
mol BDA/h