Answer :
Final Answer:
The molar flow rate of liquid water removed through condensation from the air conditioner is 13.3 mol/min, the molar flow rate of fresh air feed into the system is 486.7 mol/min,and of the recycle stream is 13.3 mol/min.
Explanation:
To analyze the overall system, we can use a degree of freedom analysis, which states that the sum of the degrees of freedom for each component in the system plus the degrees of freedom for the overall system equals the total degrees of freedom. In this case, we have one component, water (H2O), and the overall system has one degree of freedom (F = 1) since we can control either the molar flow rate of the recycle stream or the molar flow rate of the fresh air feed.
Given that the air delivered to the room contains 1.7 mol of water and the total molar flow rate of air delivered to the room is 500 mol/min, we can calculate the molar flow rate of water vapor in the delivered air:
Molar flow rate of water in delivered air = 1.7 mol
Since the molar flow rate of water in the incoming fresh air stream is 5 mol and the molar flow rate of water in the recycle stream is (2.5 - 1.7) mol, the total molar flow rate of water in the system is:
Total molar flow rate of water = 5 mol + (2.5 - 1.7) mol = 5.8 mol
The molar flow rate of liquid water removed through condensation from the air conditioner is the difference between the total molar flow rate of water in the system and the molar flow rate of water in the delivered air:
Molar flow rate of liquid water removed = 5.8 mol - 1.7 mol = 4.1 mol
Now, since the molar flow rate of the recycle stream is equal to the molar flow rate of liquid water removed through condensation (assuming no accumulation), we have:
Molar flow rate of recycle stream = 4.1 mol
The molar flow rate of fresh air feed into the system is the total molar flow rate of air delivered to the room minus the molar flow rate of the recycle stream:
Molar flow rate of fresh air feed = 500 mol/min - 4.1 mol/min = 495.9 mol/min
Thus, the molar flow rates are as follows:
Molar flow rate of liquid water removed = 4.1 mol/min
Molar flow rate of fresh air feed = 495.9 mol/min
Molar flow rate of recycle stream = 4.1 mol/min
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