Mixed Air Temperature Calculator

Created by João Rafael Lucio dos Santos, PhD
Reviewed by Dominik Czernia, PhD and Rijk de Wet
Last updated: Dec 17, 2023


You can use the mixed air temperature calculator to find the total temperature of two gases with different temperatures and concentrations. The mixed air temperature equation can also be applied to HVAC systems — so you could also use this calculator as a HVAC mixed air temperature calculator.

Do you know how to find the thermal equilibrium temperature of two gases, or how to calculate mixed air temperature? Keep reading to find out!

How to calculate the mixed air temperature

The mixed air temperature calculator computes the total temperature of two gases in thermal equilibrium with different concentrations. The mixed air temperature equation is given by:

T=T1×P1 + T2×P2\small T = T_1\times P_1\ +\ T_2\times P_2

where:

  • TT — The mixed air temperature;
  • T1T_1 — Temperature of gas 1;
  • P1P_1 — Percentage of gas 1 in the reservoir;
  • T2T_2 — Temperature of gas 2; and
  • P2P_2 — Percentage of gas 2 in the reservoir.

Remember — because these two gases are the only ones in the reservoir, the percentages P1P_1 and P2P_2 must add up to 100%.

So, the mixed air temperature formula can deliver the final temperature inside the reservoir after the gases reach thermal equilibrium.

Mixed air temperature calculator — HVAC

The mixed air temperature formula can be changed to determine the supply air temperature of a HVAC (heating, ventilation, and air conditioning) system. HVAC refers to a system that is responsible for maintaining comfortable and healthy indoor air quality.

The supply air temperature in an HVAC system is defined as the temperature of the air being delivered or supplied to the conditioned space. It is the temperature at which the air exits the HVAC system and enters the room or building.

This temperature can be determined considering the mixture of the outside air with the return air in a HVAC system. Thus, the HVAC mixed air temperature calculator is based on the following equation:

Ts=cfmoa×Toa + cfmra×Tracfmoa+cfmra\small T_s = \frac{\text{cfm}_{\rm{oa}}\times T_{\rm{oa}} \ +\ \text{cfm}_{\rm{ra}}\times T_{\rm{ra}}}{\text{cfm}_{\rm{oa}}+\text{cfm}_{\rm{ra}}}

where:

  • ToaT_{\rm{oa}} — Temperature of outside air;
  • cfmoa\text{cfm}_{\rm{oa}} — Flow rate of outside air in cubic feet per minute (cu ft / min\text{cu ft / min});
  • TraT_{\rm{ra}} — Temperature of return air;
  • cfmra\text{cfm}_{\rm{ra}} — Flow rate of return air in cubic feet per minute; and
  • TsT_{\rm{s}} — Supply air temperature, or alternatively, HVAC mixed air temperature equation result.

What is the supply air temperature to cool a house?

Let's consider that the outside air temperature is about 30°C30\text{°C} and that the typical flow rate of outside air to cool a three-bedroom house is 60 (cu ft/min)60 \rm{\ (cu\ ft/min)}. Moreover, we can assume that the total flow rate (cfmoa+cfmra\text{cfm}_{\rm{oa}}+\text{cfm}_{\rm{ra}}) supplied by the HVAC system is 1, ⁣400 (cu ft/min)1,\!400 \rm{\ (cu\ ft/min)}.

Therefore, the flow rate of return air is 1, ⁣340 (cu ft/min)1,\!340 \rm{\ (cu\ ft/min)}. If the return air temperature is about 23°C23\text{°C}, then the supply air temperature to cool a house is Ts=23.3°CT_s = 23.3\text{°C}.

💡 You can find more information about HVAC systems checking out our mixed air calculator.

How can we define the temperature of a gas?

The temperature of a gas is a measure of its thermal energy, reflecting the average kinetic energy of the gas molecules. It is a fundamental property used in various scientific and engineering calculations.

Different measurement techniques, such as thermocouples, thermometers, or thermistors, are employed to determine the temperature of gases in practical applications.

If we are considering an ideal gas, its temperature can be measured by using the ideal gas law, which is given by

PV=nRTP\,V = n \,R\,T

where:

  • PP — Pressure of the gas;
  • VV — Volume of the gas;
  • nn — Number of moles of the gas;
  • RR — Ideal gas constant, whose value is 8.31446J/(Kmol)8.31446\rm{\,J/ (K\cdot mol)}; and
  • TT — Temperature of the gas.

💡 You can learn more about the ideal gas using our ideal gas law calculator.

The concept of thermal equilibrium

The concept of thermal equilibrium refers to a state where two or more systems are at the same temperature, and there is no net transfer of heat between them. This means that the heat transfer rates from one system to another are equal, resulting in a state of thermal balance.

🔎 The thermal equilibrium is based on the Zeroth law of thermodynamics, which states that if two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.

Therefore, the Zeroth law allows us to define the concept of temperature — since if two or more bodies are in thermal equilibrium, their particles have the same average kinetic energy, and then they are at the same temperature. So, if there is a temperature difference between two or more systems, heat will flow from the hotter systems to the colder ones until thermal equilibrium is reached.

💡 More information about the kinetic energy of particles in a gas can be found in our thermal energy calculator.

The temperature can be measured using different thermodynamic scales, such as the Celsius and Kelvin scales. The Celsius scale sets the freezing point of water at 0°C and the boiling point at 100°C (at standard atmospheric pressure). On the other hand, the Kelvin scale sets absolute zero (the lowest possible temperature) at 0 Kelvin, with temperature increments equal to those on the Celsius scale.

💡 You can check more details about different thermodynamic scales using our temperature conversion.

João Rafael Lucio dos Santos, PhD
Based on gas composition
Temperature of gas 1 (T₁)
°F
Temperature of gas 2 (T₂)
°F
Percentage of gas 1 (P₁)
%
Percentage of gas 2 (P₂)
%
Mixed air temperature (T)
°F
Based on gas flow
Temperature of outside air (Tₒₐ)
°F
Temperature of return air (Tᵣₐ)
°F
Flow rate of outside air (cfmₒₐ)
ft³/min
Flow rate of return air (cfmᵣₐ)
ft³/min
Mixed air temperature (Tₛ)
°F
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