# Sensible, Latent, and Total Heat

Sensible heat is the heat that is transferred to or from a substance without causing a change in phase. It is the type of heat that we feel when we touch something that is hot or cold.

Latent heat is the heat that is transferred to or from a substance during a phase change, such as from a liquid to a gas or from a gas to a solid. It is the heat that is required to change the state of a substance without changing its temperature.

Total heat is the sum of sensible heat and latent heat. It is the total amount of heat that is transferred to or from a substance.

Equations

Sensible heat:

Sensible heat is the type of heat that we can feel and measure with a thermometer. It is the energy required to change the temperature of a substance without changing its phase (e.g., from solid to liquid or liquid to gas).

$$H_S = 1.08 \times CFM \times \Delta T$$

Latent heat:

Latent heat is the energy required to change the phase of a substance (e.g., from solid to liquid or liquid to gas). It does not cause a change in temperature.

$$H_L = 0.68 \times CFM \times \Delta W_{GR}$$

Total heat:

Total heat is the sum of sensible heat and latent heat.

$$H_T = H_S + H_L$$

where:

• HS​ is the sensible heat (Btu/hr)
• HL is the latent heat (Btu/hr)
• HT​ is the total heat (Btu/hr)
• CFM is the air flow rate (cubic feet per minute)
• ΔT is the temperature difference (°F)
• ΔWGR​ is the humidity ratio difference (grains H2O/lb. DA)

Example

An air conditioner is removing 10,000 Btu/hr of total heat from a room. The air flow rate is 1000 CFM and the temperature difference is 20°F. The humidity ratio difference is 0.005 grains H2O/lb. DA.

Sensible heat:

$$H_S = 1.08 \times 1000 \times 20 = 21,600 Btu/hr$$

Latent heat:

$$H_L = 0.68 \times 1000 \times 0.005 = 3.4 Btu/hr$$

Total heat:

$$H_T = H_S + H_L = 21,600 + 3.4 = 21,603.4 Btu/hr$$
Contents

### U-Value and Area

The U-value of a material is a measure of its thermal resistance. The lower the U-value, the better the insulation.

The area of a surface is a measure of its size.

Equation

$$H = U \times A \times \Delta T$$

where:

• H is the heat transfer rate (Btu/hr)
• U is the U-value (Btu/hr. ft². °F)
• A is the area (ft²)
• ΔT is the temperature difference (°F)

Example

A wall has a U-value of 0.25 Btu/hr.ft². °F and an area of 100 ft². The temperature difference between the inside and outside of the wall is 20°F.

Heat transfer rate:

$$H = 0.25 \times 100 \times 20 = 500 Btu/hr$$

### Sensible Heat Ratio (SHR)

The sensible heat ratio (SHR) is the ratio of sensible heat to total heat. It is a measure of how much of the total heat is sensible heat.

Equation

$$SHR = \frac{H_S}{H_T} = \frac{H_S}{H_S + H_L}$$

Example

In the previous example, the sensible heat is 21,600 Btu/hr and the total heat is 21,603.4 Btu/hr. Therefore, the SHR is:

$$SHR = \frac{21,600}{21,603.4} = 0.999$$

Conclusion

Sensible, latent, and total heat are important concepts in HVAC. By understanding these concepts, you can better design and operate HVAC systems.