2D7 :  Humid Air and Relative Humidity  6 pts 

Air is
fed to a furnace at a volumetric flow rate of 745 m^{3}/h. The air is at 50^{o}C, 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  ^{o}C  Find :  n_{H2O}  ???  mol H_{2}O/h  
P  100  kPa  n_{BDA}  ???  mol BDA/h  
h_{R}  37%  
V_{dot}  745  m^{3}/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 y_{BDA} . 

Eqn 4  
So, we need to determine n_{total} and y_{H2O} 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/molK  n_{total}  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 50^{o}C in the Saturated Temperature Table of the Steam Tables.  P*_{H2O}  38.595  kPa  
Now, plug values back into Eqn 8 :  y_{H2O}  0.1428  mol H_{2}O/mol  
Finally, plug values into Eqns 1, 4 & 2 :  n_{H2O}  3960  mol H_{2}O/h  
y_{BDA}  0.8572  mol BDA/mol  
n_{BDA}  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 :  n_{H2O}  3960  mol H_{2}O/h  n_{BDA}  23800  mol BDA/h 