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Air Filtration, Solar Panel, and Peltier Module Calculations

Air Filtration System Design

Step 1: Calculate the Room's Air Volume

The room's air volume helps to determine how much air needs to be filtered.

• Room dimensions: 10 feet x 10 feet x 8 feet (assuming a standard ceiling height of 8 feet).

• Room volume:

  $$\text{Room Volume} = 10 \, \text{ft} \times 10 \, \text{ft} \times 8 \, \text{ft} = 800 \, \text{cubic feet (cu.ft)}$$

Step 2: Determine Required Air Changes per Hour (ACH)

Air changes per hour (ACH) vary based on the room's purpose:

• ACH for general air filtration: 4-6 ACH.
• Rooms with higher air quality demands: 6-10 ACH.
• For this case, we will assume 6 ACH.

This means the entire air volume in the room should be filtered 6 times per hour.

Step 3: Calculate Required Airflow (CFM)

Airflow is measured in cubic feet per minute (CFM).

1. Total air to be filtered per hour:

   $$\text{Air Volume} \times \text{ACH} = 800 \, \text{cu.ft} \times 6 = 4800 \, \text{cu.ft/hour}$$

2. Convert to minutes: To determine CFM, divide by 60 (minutes in an hour):

   $$\text{CFM} = \frac{4800 \, \text{cu.ft/hour}}{60} = 80 \, \text{CFM}$$

Step 4: Filter Size

You have 8 filters (4 HEPA and 4 carbon filters), each with a size of 1 square foot.

• Total filter area:

  $$\text{Total Filter Area} = 4 \times 1\, \text{sq.ft (HEPA)} + 4 \times 1\, \text{sq.ft (Carbon)} = 8 \, \text{sq.ft}$$

• HEPA filter rating: 100-150 CFM per square foot.

• Carbon filter rating: 50-100 CFM per square foot.

Step 5: Fan Power Estimation

To match the required airflow of 80 CFM, the fan should overcome the resistance from the filters.

• Assume moderate pressure drop of 1.0 inches of water.
• Fan power estimate: 1 CFM per 1 watt, so approximately 80-100 watts would be needed for the fan.

Conclusion

• Required fan power: 80-100 watts.
• Filter size: Total of 8 sq.ft with 4 HEPA and 4 carbon filters.
• Fan airflow: 80 CFM.

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Solar Panel and Battery Charging

Step 1: Key Parameters

• Solar panel power: 20 watts.
• Battery capacity: 7 Ah (12V battery).
• Voltage: 12V system.

Step 2: Energy Required to Charge the Battery

Convert the amp-hour (Ah) rating to watt-hours (Wh):

$$\text{Battery capacity} = 7 \, \text{Ah} \times 12 \, \text{V} = 84 \, \text{Wh}$$

Step 3: Solar Panel Output

Determine the panel output in amps:

$$\text{Panel output} = \frac{20 \, \text{watts}}{12 \, \text{V}} = 1.67 \, \text{amps}$$

Step 4: Charging Time Calculation

Calculate the time to fully charge the battery:

$$\text{Charging time} = \frac{84 \, \text{Wh}}{20 \, \text{W}} = 4.2 \, \text{hours}$$

Step 5: Real-World Considerations

Considering real-world factors (like sunlight variability):

• Assume 5 hours of good sunlight per day.

• Daily charge capacity:

  $$1.67 \, \text{amps} \times 5 \, \text{hours} = 8.35 \, \text{Ah/day}$$

This means the panel could theoretically fully charge the battery in one day under good sunlight conditions.

Conclusion

• Ideal charging time: 4.2 hours in perfect conditions.
• Real-world charging time: 5-6 hours of sunlight.
• Optimal direction: Panel should face south (north if in southern hemisphere) with a tilt angle matching the latitude.

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Peltier Module Heating and Cooling

Step 1: Key Specifications

• Room dimensions: 10 feet x 10 feet x 8 feet (800 cubic feet).
• Peltier modules:

  • Current rating: 6 amps per module.

  • Number of modules: 4.

  • Voltage: 12V.

  • Power per module:

    $$6 \, \text{amps} \times 12 \, \text{volts} = 72 \, \text{watts/module}$$

  • Total power:

    $$72 \, \text{watts/module} \times 4 = 288 \, \text{watts total}$$

Step 2: Cooling/Heating Power (Q)

Each Peltier module provides 50% efficiency for cooling or heating:

$$\text{Cooling power/module} = 72 \, \text{watts} \times 0.5 = 36 \, \text{watts}$$ $$\text{Total cooling/heating power} = 36 \, \text{watts} \times 4 = 144 \, \text{watts}$$

Step 3: Heat Load Estimation (Cooling)

Assume a 10°C (18°F) temperature drop. The specific heat capacity of air is 0.018 BTU per cubic foot per °F. Total heat energy to remove:

$$Q = 800 \, \text{cu.ft} \times 0.018 \, \text{BTU/°F} \times 18 \, \text{°F} = 259.2 \, \text{BTU}$$ $$\text{Convert to watts} = 259.2 \, \text{BTU} \times 0.293 \, \text{watts/BTU} = 75.96 \, \text{watts}$$

Step 4: Cooling/Heating Time Calculation

Calculate the cooling time:

$$\text{Time} = \frac{75.96 \, \text{watt-hours}}{144 \, \text{watts}} \approx 0.53 \, \text{hours} \approx 32 \, \text{minutes}$$

The same calculation applies for heating, so the time to heat the room by 10°C is also approximately 32 minutes.

Conclusion

• Cooling time: ~32 minutes.
• Heating time: ~32 minutes.
• Real-world factors like insulation and Peltier module efficiency may affect performance.