# Example Problem with Complete Solution

2D-7 : Humid Air and Relative Humidity 6 pts
Air is fed to a furnace at a volumetric flow rate of 745 m3/h. The air is at 50oC, 100 kPa and has a relative humidity of 37%.
a.) Calculate the molar flow rate of bone dry air (BDA) into the furnace in mole/h.
b.) Calculate the molar flow rate of water (within the humid air) into the furnace in mole/h.

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 50 oC Find : nH2O ??? mol H2O/h
P 100 kPa nBDA ??? mol BDA/h
hR 37%
Vdot 745 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 :
Eqn 1 Eqn 2
Because humid air is made up of bone dry air (BDA) and water, only : Eqn 3
Solve Eqn 3 for yBDA . 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: Eqn 5
Solve Eqn 5 for the total molar flow rate. Eqn 6
R 8.314 J/mol-K ntotal 27730 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.
Eqn 7
We can now solve Eqn 7 for the mole
fraction of water in the humid air.
Eqn 8
We can look up the vapor pressure of water at 50oC in the Saturated Temperature Table of the Steam Tables. P*H2O 38.595 kPa
Now, plug values back into Eqn 8 : yH2O 0.1428 mol H2O/mol
Finally, plug values into Eqns 1, 4 & 2 : nH2O 3960 mol H2O/h
yBDA 0.8572 mol BDA/mol
nBDA 23770 mol BDA/h
Verify : The ideal gas assumption needs to be verified.
We need to determine the specific volume and check if :
Eqn 9
V 26.87 L/mol The ideal gas assumption is valid because V > 20 L/mole.
Answers : nH2O 3960 mol H2O/h nBDA 23800 mol BDA/h