1.3 Principles of Heat Transfer, Temperature Scales, and Heat Quantity Calculations

Principles of Heat Transfer, Temperature Scales, and Heat Quantity Calculations

Thermodynamics governs all heating, ventilation, air conditioning, and refrigeration processes. Air conditioning is not the addition of cold, but rather the removal of heat energy from a conditioned space and its rejection to an external sink.

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Fundamental Laws of Thermodynamics

HVAC engineering rests upon two core thermodynamic principles:

1. First Law of Thermodynamics (Conservation of Energy): Energy cannot be created or destroyed, only converted from one form to another. In a refrigeration system, electrical energy input to the compressor motor plus heat absorbed in the evaporator equals the total heat rejected at the condenser ($Q_{\text{condenser}} = Q_{\text{evaporator}} + W_{\text{compressor}}$).
2. Second Law of Thermodynamics: Heat flows naturally and spontaneously from a warmer body (higher thermal intensity) to a cooler body (lower thermal intensity). Heat will never flow from a cold object to a hot object without external work being applied (work input by the compressor).

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The Three Modes of Heat Transfer

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Temperature Scales & Conversions

Temperature measures the intensity of heat (average kinetic energy of molecules), whereas heat quantity measures total thermal energy contained in a mass.

Scale Definitions

• Fahrenheit (°F): Imperial scale where water freezes at $32^\circ\text{F}$ and boils at $212^\circ\text{F}$ under standard atmospheric pressure ($14.696 \text{ psia}$).
• Celsius (°C): Metric scale where water freezes at $0^\circ\text{C}$ and boils at $100^\circ\text{C}$.
• Kelvin (K): Absolute metric scale where $0 \text{ K}$ represents absolute zero (complete cessation of molecular motion).
• Rankine (°R): Absolute Imperial scale where $0^\circ\text{R}$ represents absolute zero ($-459.67^\circ\text{F}$).

Temperature Conversion Equations

$$\text{Fahrenheit to Celsius: } ^\circ\text{C} = \frac{^\circ\text{F} - 32}{1.8}$$ $$\text{Celsius to Fahrenheit: } ^\circ\text{F} = (^\circ\text{C} \times 1.8) + 32$$ $$\text{Kelvin: } \text{K} = ^\circ\text{C} + 273.15$$ $$\text{Rankine: } ^\circ\text{R} = ^\circ\text{F} + 459.67$$

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Heat Quantity Definitions: BTU & Ton of Refrigeration

• British Thermal Unit (BTU): The amount of heat energy required to raise the temperature of 1 pound of pure liquid water by 1°F (specifically from $59.5^\circ\text{F}$ to $60.5^\circ\text{F}$).
• Ton of Refrigeration: The cooling capacity equivalent to the heat absorbed by melting 1 ton ($2,000 \text{ lbs}$) of pure ice at $32^\circ\text{F}$ into liquid water at $32^\circ\text{F}$ over a period of 24 hours.

$$\text{Latent Heat of Fusion of Water} = 144 \text{ BTU/lb}$$ $$\text{Total Latent Heat} = 2,000 \text{ lbs} \times 144 \text{ BTU/lb} = 288,000 \text{ BTU per 24 hours}$$ $$\text{Hourly Cooling Rate} = \frac{288,000 \text{ BTU}}{24 \text{ hours}} = \mathbf{12,000 \text{ BTU/hr per Ton}}$$

Electrical Heat Equivalent: $1 \text{ Watt} = 3.412 \text{ BTU/hr}$. A $5 \text{ kW}$ electric resistance heating element produces $5,000 \times 3.412 = 17,060 \text{ BTU/hr}$.

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Sensible Heat, Latent Heat, and Enthalpy

Thermal calculations require separating temperature-changing heat from phase-changing heat.

Sensible Heat ($Q_s$)

Sensible heat added to or removed from a substance produces a direct change in temperature that can be measured with a standard dry-bulb thermometer. No phase change occurs.

$$Q_s = m \times c \times \Delta T$$

Where $m$ is mass (lbs), $c$ is specific heat capacity ($\text{BTU/lb}\cdot^\circ\text{F}$), and $\Delta T$ is temperature change ($^\circ\text{F}$).

• Specific Heat Capacity ($c$): The heat required to raise 1 lb of a substance by 1°F.
  • Water: $1.00 \text{ BTU/lb}\cdot^\circ\text{F}$
  • Ice: $0.50 \text{ BTU/lb}\cdot^\circ\text{F}$
  • Steam: $0.48 \text{ BTU/lb}\cdot^\circ\text{F}$
  • Standard Air: $0.24 \text{ BTU/lb}\cdot^\circ\text{F}$

Latent Heat ($Q_l$)

Latent heat added to or removed from a substance causes a change of state (phase change) with no change in temperature.

• Latent Heat of Fusion: Heat required to change a solid to a liquid at its melting point ($144 \text{ BTU/lb}$ for water at $32^\circ\text{F}$).
• Latent Heat of Vaporization: Heat required to change a liquid to a vapor at its boiling point ($970.4 \text{ BTU/lb}$ for water at $212^\circ\text{F}$ at sea level).

Total Heat / Enthalpy ($h$)

Enthalpy is the total heat content of a substance above an arbitrary baseline ($0^\circ\text{F}$ for refrigerants), combining both sensible and latent heat quantities ($h = Q_s + Q_l$).

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Practical HVAC Field Calculations

Technicians calculate sensible, latent, and total heat rates for air and water streams using empirical field formulas.

Sensible Heat Formula for Airflow

$$Q_{\text{sensible}} = 1.08 \times \text{CFM} \times \Delta T$$

Derivation of Constant 1.08:

$$\text{Density of Standard Air} = 0.075 \text{ lbs/ft}^3$$ $$\text{Specific Heat of Air} = 0.24 \text{ BTU/lb}\cdot^\circ\text{F}$$ $$\text{Minutes per Hour} = 60$$ $$\text{Constant} = 0.075 \times 0.24 \times 60 = \mathbf{1.08}$$

Latent Heat Formula for Airflow

$$Q_{\text{latent}} = 0.68 \times \text{CFM} \times \Delta W_{\text{grains}}$$

Where $\Delta W_{\text{grains}}$ is the moisture content difference in grains of moisture per pound of dry air ($7,000 \text{ grains} = 1 \text{ lb of water}$).

Total Heat Formula for Airflow & Sensible Heat Ratio

$$Q_{\text{total}} = 4.5 \times \text{CFM} \times \Delta h$$

Where $\Delta h$ is the enthalpy change in BTU/lb of dry air, derived from psychrometric wet-bulb temperatures. The Sensible Heat Ratio (SHR) indicates the proportion of total cooling that addresses sensible load:

$$\text{SHR} = \frac{Q_{\text{sensible}}}{Q_{\text{total}}}$$

Hydronic Water Flow Sensible Heat Formula

$$Q_{\text{water}} = 500 \times \text{GPM} \times \Delta T$$

Where GPM is Gallons Per Minute and 500 represents ($8.33 \text{ lbs/gal} \times 60 \text{ min/hr} \times 1.0 \text{ sp. heat}$).