# Mixed Air Temperature Calculator

Table of contents

How to calculate the mixed air temperatureMixed air temperature calculator — HVACWhat is the supply air temperature to cool a house?How can we define the temperature of a gas?The concept of thermal equilibriumYou 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:

where:

- $T$ — The mixed air temperature;
- $T_1$ — Temperature of gas 1;
- $P_1$ — Percentage of gas 1 in the reservoir;
- $T_2$ — Temperature of gas 2; and
- $P_2$ — Percentage of gas 2 in the reservoir.

Remember — because these two gases are the only ones in the reservoir, the percentages $P_1$ and $P_2$ 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:

where:

- $T_{\rm{oa}}$ — Temperature of outside air;
- $\text{cfm}_{\rm{oa}}$ — Flow rate of outside air in cubic feet per minute ($\text{cu ft / min}$);
- $T_{\rm{ra}}$ — Temperature of return air;
- $\text{cfm}_{\rm{ra}}$ — Flow rate of return air in cubic feet per minute; and
- $T_{\rm{s}}$ — 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 $30\text{°C}$ and that the typical **flow rate of outside air** to cool a three-bedroom house is $60 \rm{\ (cu\ ft/min)}$. Moreover, we can assume that the **total flow rate** ($\text{cfm}_{\rm{oa}}+\text{cfm}_{\rm{ra}}$) supplied by the HVAC system is $1,\!400 \rm{\ (cu\ ft/min)}$.

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

💡 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

where:

- $P$ — Pressure of the gas;
- $V$ — Volume of the gas;
- $n$ — Number of moles of the gas;
- $R$ — Ideal gas constant, whose value is $8.31446\rm{\,J/ (K\cdot mol)}$; and
- $T$ — 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.