Consider an air conditioner operating in a recycle system mode where fresh air is taken from the ambient atmosphere to be cooled and dehumidified before being delivered to a room. The fresh air from the atmosphere contains 5 moles of water. This fresh air stream is then mixed with the recycle stream, resulting in a stream that contains 2.5 moles of water. This stream, after mixing, is led into the air conditioner unit, where a fraction of water is condensed and removed as liquid. The remaining stream contains 1.7 moles of water and is taken out and fed into a splitter. One stream from the splitter is taken as the recycle stream, while the other is delivered to the room. The air delivered to the room contains 1.7 moles of water.

Tasks:

1. Draw a labeled flowchart for the system.
2. Perform a degree of freedom analysis for the overall system, mixer, air conditioner, and splitter.
3. Determine:
- The molar flow rate of liquid water removed through condensation from the air conditioner.
- The molar flow rate of the fresh air feed into the system.
- The molar flow rate of the recycle stream.

Assume that 500 moles/minute of air (containing 1.7 moles of water) is delivered to the room.

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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