When repurposing conditioned air from a manufacturing floor for server cooling, we must apply the fundamental heat transfer equation:

Q = m × Cp × ΔT
where:
Q = heat energy (BTU/hr)
m = mass flow rate of air (lb/hr)
Cp = specific heat of air (0.24 BTU/lb-°F)
ΔT = temperature difference between exhaust and intake (°F)

For your specific case with 5000 BTU/hr heat load and 800 ft³ closet volume:

// Convert BTU/hr to CFM (cubic feet per minute)
function calculateRequiredCFM(btuPerHour, tempRiseF) {
    const airDensity = 0.075; // lb/ft³ at sea level
    const specificHeat = 0.24; // BTU/lb-°F
    const minutesPerHour = 60;
    
    return btuPerHour / (airDensity * specificHeat * tempRiseF * minutesPerHour);
}

// Example calculation for 10°F temperature rise
const requiredCFM = calculateRequiredCFM(5000, 10);
console.log(Required CFM: ${requiredCFM.toFixed(2)});

For server environments, we typically want at least 10-15 complete air changes per hour. With your 800 ft³ space:

const roomVolume = 800; // ft³
const desiredACH = 12; // air changes per hour
const requiredCFMForACH = (roomVolume * desiredACH) / 60;

console.log(CFM for ${desiredACH} ACH: ${requiredCFMForACH.toFixed(2)});

You'll want a fan that meets both the thermodynamic CFM requirement and air exchange rate. Key parameters:

• Static pressure capability (typically 0.1-0.25" H₂O for small closets)
• Acoustic performance (aim for <50 dBA for manufacturing environments)
• Filter compatibility (MERV 8 minimum for dust protection)

Here's a complete Node.js module for server closet calculations:

class ServerClosetCooling {
    constructor(roomVolumeFt3, btuPerHour, maxTempRiseF, desiredACH) {
        this.roomVolume = roomVolumeFt3;
        this.btuPerHour = btuPerHour;
        this.maxTempRise = maxTempRiseF;
        this.desiredACH = desiredACH;
    }

    calculateThermodynamicCFM() {
        return this.btuPerHour / (1.08 * this.maxTempRise);
    }

    calculateAirExchangeCFM() {
        return (this.roomVolume * this.desiredACH) / 60;
    }

    getRequiredCFM() {
        return Math.max(
            this.calculateThermodynamicCFM(),
            this.calculateAirExchangeCFM()
        );
    }
}

// Usage example
const closet = new ServerClosetCooling(800, 5000, 10, 12);
console.log(Recommended CFM: ${closet.getRequiredCFM().toFixed(2)});

After installation, implement temperature monitoring to validate performance:

// Python example for temperature monitoring
import time
from sensors import TemperatureSensor

intake_sensor = TemperatureSensor(pin=4)
exhaust_sensor = TemperatureSensor(pin=5)

def monitor_closet():
    while True:
        delta_temp = exhaust_sensor.read() - intake_sensor.read()
        print(f"Current ΔT: {delta_temp:.1f}°F")
        if delta_temp > 15:  # Threshold exceeded
            alert_administrator()
        time.sleep(300)  # Check every 5 minutes

For server room cooling calculations, we use the fundamental HVAC formula:

CFM = (BTU/hr) / (1.08 × ΔT)

Where:
- BTU/hr = Total heat output of equipment (5000 BTU/hr in your case)
- ΔT = Temperature difference between intake and exhaust air (in °F)
- 1.08 = Constant combining air density and specific heat

Here's how you'd implement this as a reusable function:

def calculate_required_cfm(btu_per_hour, temp_difference):
    """
    Calculate required CFM for server room cooling
    :param btu_per_hour: Total heat output in BTU/hr
    :param temp_difference: Desired ΔT between intake and exhaust (°F)
    :return: Required CFM
    """
    return btu_per_hour / (1.08 * temp_difference)

# Example usage for your case:
required_cfm = calculate_required_cfm(5000, 10)  # Assuming 10°F ΔT
print(f"Required CFM: {required_cfm:.2f}")

For your 800 ft³ room, we should also verify air exchange rates:

def calculate_air_exchanges(cfm, room_volume):
    """
    Calculate air exchanges per hour
    :param cfm: Cubic feet per minute of airflow
    :param room_volume: Room volume in cubic feet
    :return: Air exchanges per hour
    """
    return (cfm * 60) / room_volume

# Using our previous calculation:
exchanges_per_hour = calculate_air_exchanges(required_cfm, 800)
print(f"Air exchanges per hour: {exchanges_per_hour:.1f}")

In practice, you'll need to account for:

• Heat stratification (hot air rises)
• Equipment layout and airflow obstruction
• Future expansion capacity

A good safety margin is to multiply your calculated CFM by 1.2-1.5:

adjusted_cfm = required_cfm * 1.3
print(f"Adjusted CFM with safety margin: {adjusted_cfm:.2f}")

When selecting your exhaust fan, consider:

fan_specs = {
    'static_pressure': 0.1,  # inches of water (typical for small rooms)
    'efficiency': 0.7,      # typical for inline fans
    'noise_level': '<45 dB' # important for office environments
}