# Charles' Law Calculator

Created by Davide Borchia
Last updated: Jul 23, 2022

Volume, temperature, and pressure are the most important quantities used to describe a gas: our Charles' law calculator will teach you one of the three fundamental gas laws, the law for the temperature and the volume of a gas.

• A brief introduction to the mathematics of ideal gases;
• What is Charles' law;
• Why is there an equation for the temperature and volume of gas;
• How to calculate Charle's law; and
• Some examples of Charles law in real life.

## The math of ideal gases

Gases are not so easy to describe: with their freely moving molecules, things get complicated pretty quickly. However, physicists discovered an extremely helpful set of mathematical laws for extremely low-density gases: the ideal gas laws. These laws combine in an easy and immediate way the three defining quantities of a gas:

• Pressure;
• Temperature; and
• Volume.

🙋 The low-density requirement stems from the fact that intermolecular forces can affect the physical parameter of a gas. The fewer the molecules, the fewer the interactions: from here to assume ideality, the step is short.

There are three fundamental gas laws:

• The Boyle's law;
• The Gay-Lussacs' law; and
• The Charles law.

Each of them deals with only two variables, while the last one remains constant. We can identify three possible processes: isothermic (constant temperature), isobaric (constant pressure), and isochoric (constant volume). In our Charles' law calculator, we will discover constant pressure processes. Let's go!

You can join all three ideal gas laws in a single expression where no parameters are fixed. The result is a handy and generalized expression with widespread use both in chemistry and physics. Find more about it at our combined gas law calculator.

## What is Charles' law of gases? The law for volume and temperature of a gas

Charles' law allows you to calculate the volume of a gas as a function of the temperature (and vice-versa). Assuming that the pressure is constant, we can state the volume-temperature equation for a gas as:

$\frac{V}{T}=k$

Where:

• $V$ is the volume of the gas;
• $T$ is the temperature measured in kelvin; and
• $k$ is Charles' law constant.

Constant pressure is a common occurrence in nature. Actually, it may be the most common occurrence. Volumes can change, and temperature is subjected to many small local variations: we live, instead, in a pretty uniform pressure, with variations often on a larger scale. Whenever a process happens with an "open door", you know it's an isobaric process!

Under Charles' law, the volume and the temperature of a gas are in a linear relationship: if we plot these two quantities, we will find a line departing from the origin and growing with slope equal to Charles' law constant, $k$.

The explanation of Charles' law lies in the microscopic nature of a gas: a great number of molecules traveling in a container. The temperature of the gas determines the kinetic energy of the molecules. The higher the temperature, the higher the kinetic energy, which means a higher speed. If we fix the volume of the container, we would have more collisions in a unit time (hence an increased pressure). If the volume is free to change, the pressure would equalize (same number of collisions) but the distance covered by each molecule would increase (increased volume).

## How to calculate Charles' law

Usually, we don't calculate Charles' law constant $k$, but we take the quantities at two different moments of a process to compute any missing parameters. If we know the initial temperature and volume of a gas, calculating the final quantities is straightforward:

$\frac{V_1}{T_1}=\frac{V_2}{T_2}$

Where the subscripts indicate the "points" of a process at which we measured these quantities. As you can easily see, if you know three of those values you can calculate the fourth in the blink of an eye: our Charles' law calculator does exactly this!

## Examples of Charles' law in everyday life

You'd be surprised to know that Charles' law for the temperature and volume of a gas can be easily found (and proved) without the need for any particular instrument.

Hot air balloons are a good example and are also pretty nice. The beautiful and colorful balloons are open at the bottom: the pressure is thus equal on the inside and on the outside. The pilot warms the air inside the balloon, and thanks to Charles' law, its volume increase. The density of the air inside the balloon decreases, and the buoyant force increases. Are you ready for the ascent?

To prove in an elegant and simple way Charles' law, inflate a party balloon and seal it tightly. The balloon is now just slightly overpressurized (due to the surface tension of the material), but in equilibrium with the environment. Now open the freezer, and put the balloon in it: the pressure won't change (unless your freezer is really weird). Leave the balloon there for a while. When you reopen the freezer, you will find that the balloon shrank. Why? Well, the temperature decreased, and as a consequence of Charles' law, the volume did the same!

Davide Borchia
Initial parameters
Initial volume (V₁)
Initial temperature (T₁)
K
Final parameters
Final volume (V₂)
Final temperature (T₂)
K
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