Cooling Heating Equations

Overview

Engineering reference data for Cooling Heating Equations in HVAC systems.

Key Formulas

Sensible Heat

$Q = \dot{m} c_p \Delta T$

Heat causing temperature change.

Latent Heat

$Q = \dot{m} h_{fg} \Delta\omega$

Heat causing moisture change.

COP (Cooling)

$COP = Q_c / W$

Coefficient of performance.

Variables

Worked Examples

Sensible Heat — Metric

An air flow of 1 m³/s is heated from 0°C to 20°C. Using the sensible heat equation:

$h_s = c_p \rho q \Delta t$

h_s = (1.006 \text{ kJ/kg°C}) \times (1.202 \text{ kg/m^{3}}) \times (1 \text{ m^{3}/s}) \times (20°C - 0°C) = 24.2 \text{ kW}

Sensible Heat — Imperial

An air flow of 1 cfm is heated from 32°F to 52°F:

$h_s = 1.08 \times q \times \Delta t$

$h_s = 1.08 \times 1 \text{ cfm} \times (52°F - 32°F) = 21.6 \text{ Btu/hr}$

Latent Heat — Metric

An air flow of 1 m³/s is cooled from 30°C to 10°C. Relative humidity starts at 70% and ends at 100%. From the Mollier diagram: inlet humidity = 0.0187 kg/kg dry air, outlet humidity = 0.0075 kg/kg dry air.

$h_l = \rho h_{we} q \Delta w_{kg}$

$h_l = (1.202)(2454)(1)(0.0187 - 0.0075) = 34.3 \text{ kW}$

Latent Heat — Imperial

An air flow of 1 cfm is cooled from 52°F to 32°F. Humidity starts at 40 grains/lb dry air, ends at 26 grains/lb dry air:

$h_l = 0.68 \times q \times \Delta w_{gr}$

$h_l = 0.68 \times 1 \times (40 - 26) = 9.5 \text{ Btu/hr}$

Total Heat — Metric

Using the same cooling scenario, enthalpy from the Mollier diagram: inlet = 77 kJ/kg dry air, outlet = 28 kJ/kg dry air:

$h_t = \rho q \Delta h$

$h_t = (1.202)(1)(77 - 28) = 58.9 \text{ kW}$

Total Heat — Imperial

Same scenario using psychrometric chart values: inlet enthalpy = 18.7 Btu/lb, outlet = 11.8 Btu/lb:

$h_t = 4.7 \times q \times \Delta h$

$h_t = 4.7 \times 1 \times (18.7 - 11.8) = 32.4 \text{ Btu/hr}$

Sensible Heat Ratio (SHR)

The Sensible Heat Ratio expresses the fraction of total cooling/heating load that is sensible:

$SHR = \frac{h_s}{h_t} = \frac{h_s}{h_s + h_l}$

A lower SHR indicates higher dehumidification relative to temperature reduction — important for selecting cooling coils and designing humidity control strategies.

Key Constants — SI vs Imperial

The simplified Imperial constants (1.08, 0.68, 4.7) bundle air density and specific heat into single multipliers for quick calculations at standard conditions.

Temperature-dependent latent heat of evaporation:

$h_{we} = 2494 - 2.2 \, t$

where $t$ is the evaporation temperature in °C.

Unit conversion: 1 grain = 0.000143 lb = 0.0648 g

References

• Original Source