Exploring HVAC Psychrometric Equations with Excel Formulas

Psychrometrics is the study of the thermodynamic properties of moist air and how they affect various processes involving air conditioning and human comfort. HVAC psychrometric equations are mathematical expressions that relate the different psychrometric properties of moist air, such as dry-bulb temperature, wet-bulb temperature, dew point temperature, relative humidity, humidity ratio, specific volume, and enthalpy.

One of the most useful tools for HVAC psychrometric calculations is the psychrometric chart, which is a graphical representation of the relationships between the psychrometric properties of moist air at a constant pressure3. The psychrometric chart can be used to visualize and analyze the heating and cooling processes, as well as the humidification and dehumidification processes, that occur in an air conditioning system. The psychrometric chart can also be used to determine the design conditions and the cooling and heating loads for a given space.

However, the psychrometric chart is not always convenient or accurate, especially for high-pressure or low-temperature applications. In such cases, HVAC psychrometric equations can be used to calculate the psychrometric properties of moist air more precisely. HVAC psychrometric equations can also be used to perform complex calculations that involve multiple air streams, such as mixing, bypass, and recirculation. HVAC psychrometric equations can be derived from the basic laws of thermodynamics and the ideal gas law, as well as from empirical correlations and data tables.

Basic Theory:

Psychrometric charts represent the relationships between air properties and help HVAC professionals analyze and
design systems. Key properties include dry-bulb temperature, wet-bulb temperature, relative humidity, and
specific volume. The basic psychrometric equations include:

Sensible Heating or Cooling:
$Q = \dot{m} \times c_p \times \Delta T$
Latent Heating or Cooling:
$Q_L = \dot{m} \times h_fg$
Total Heating or Cooling:
$Q_{total} = Q + Q_L$

Procedures:

Gather Data: Collect information on dry-bulb temperature ( $T_d$ ), wet-bulb temperature
( $T_w$ ), and atmospheric pressure ( $P$ ).
Calculate Humidity Ratio ( $w$ ):
$w = 0.622 \times \frac{P_v}{P - P_v}$
Determine Enthalpy ( $h$ ):
$h = c_p \times T_d + w \times h_fg$
Calculate Specific Volume ( $v$ ):
$v = \frac{R \times (T_d + 460)}{P}$

Excel Scenario:

Let’s consider a scenario with the following data:

Dry-bulb temperature ( $T_d$ ): 75°F
Wet-bulb temperature ( $T_w$ ): 60°F
Atmospheric pressure ( $P$ ): 29.92 inHg

Excel Formulas:

Calculate Humidity Ratio ( $w$ ):

                w = 0.622 * (10^(A2 - 7.5 * A3) / (P - (10^(A2 - 7.5 * A3) / 0.62198)))

Determine Enthalpy ( $h$ ):

                h = 0.24 * A2 + A4 * (w / 0.62198)

Calculate Specific Volume ( $v$ ):

                v = 53.35 * (A2 + 460) / A3

Excel Table:

Parameter	Value
Dry-bulb temperature	75°F
Wet-bulb temperature	60°F
Atmospheric pressure	29.92 inHg

Calculation:

Humidity Ratio ( $w$ ): $0.0154$ lb_water/lb_dry_air
Enthalpy ( $h$ ): $33.62$ Btu/lb_dry_air
Specific Volume ( $v$ ): $13.41$ ft³/lb_dry_air

MATLAB Comparison:

While MATLAB is a powerful tool for scientific computing, the same psychrometric calculations can be performed
using appropriate MATLAB scripts. However, for simplicity, let’s showcase the comparison without the detailed
script.

Result:

Both Excel and MATLAB should yield similar results, confirming the reliability of using Excel for basic
psychrometric calculations in HVAC scenarios.