# Charles' Law Calculator

By Wojciech Sas, PhD candidate
Last updated: May 18, 2020

The Charles' law calculator is a simple tool which describes the basic parameters of an ideal gas in an isobaric process. In the text, you can find the answer to the question "What is Charles' law?", learn what the Charles' law formula looks like, and read how to solve thermodynamic problems with some Charles' law examples.

## Charles' law definition

Charles' law (sometimes referred to the law of volumes) describes the relationship between the volume of a gas and its temperature when the pressure and the mass of the gas is constant. It states that the volume is proportional to the absolute temperature.

There are a few other ways we can write the Charles' law definition, one of which is: the ratio of the volume and the temperature of the gas in a closed system is constant as long as the pressure is unchanged.

Charles' law describes the behavior of an ideal gas during an isobaric process, which means that the pressure remains constant during the transition.

## Charles' law formula Based on the definition of Charles' law, we can write the Charles' law equation in the following way:

`V₁ / T₁ = V₂ / T₂`,

where `V₁` and `T₁` are initial volume and temperature, respectively. Similarly, `V₂` and `T₂` are the final values of these gas parameters.

How does this Charles' law calculator work? First, you need to insert three of the parameters, and the fourth one is calculated for you automatically. Let's say we want to find the final volume, then the Charles' law formula yields: `V₂ = V₁ / T₁ * T₂`.

If you prefer to set the final volume and want to estimate the resulting temperature, then the equation of Charles' law changes to:

`T₂ = T₁ / V₁ * V₂`.

In advanced mode, you can also define the pressure and see how many moles of atoms or molecules there are in a container.

## Charles' law examples

We can use Charles' law calculator to solve some thermodynamic problems. Let's see how it works:

1. Imagine that we have a ball pumped full of air. Its initial volume is equal to `2 liters`, and it's placed on a beach where the temperature is `35°C`. We then move it to an air-conditioned room with a temperature of `15°C`. How does the volume of the ball change?
• First of all, the Charles' law formula requires the absolute values of temperatures, so that we have to convert them into Kelvin: `T₁ = 35°C = 308.15 K`, `T₂ = 15°C = 288.15 K`

• Then we can apply the Charles' law equation in the form where the final volume is being evaluated: `V₂ = V₁ / T₁ * T₂ = 2 l / 308.15 K * 288.15 K = 1.8702 l`.

As we can see, the volume decreases when the ball is moved from warmer to a cooler place. Sometimes you can experience that effect while changing your location or simply leaving an object alone when the weather turns. The ball seems to be under-inflated, and somebody may think that there is a hole, causing the air to leak. Fortunately, it's only physics, so you don't have to buy another ball - just inflate the one you have and enjoy! One tiny remark - air is an example of a real gas, so the outcome is only an approximation, but as long as we avoid extreme conditions (pressure, temperature). The result is sufficiently close to the actual value.

1. In the second problem, we heat an easily-stretched container. It's filled with nitrogen, which is a good approximation of an ideal gas. We can find that its initial volume is `0.03 ft³` at room temperature, `295 K`. Then we put it close to the heating source, and leave it for a while. After a few minutes, its volume has increased to `0.062 ft³`. With all of this data, can we estimate the temperature of our heater?
• Let's apply the Charles' law formula and rewrite in the form so that the temperature can be worked out: `T₂ = T₁ / V₁ * V₂ = 295 K * 0.03 ft³ / 0.062 ft³ = 609.7 K`.

• The outcome can be written in more amiable form `T₂ = 336.55°C` or `T₂ = 637.79°F`.

This is a great example which shows us that this kind of device can be used as a thermometer! Well, it's not a very practical method, and is probably not as precise as the common ones, but it still makes you think, what other unusual applications can you get from other everyday objects?

## What is Charles' law application in real life?

There are actually various areas where we can use Charles' law. Here is a list of a few of the most popular and most interesting examples:

• Balloon flight - you must have seen a balloon in the sky at least once in your life. Have you ever wondered how is it possible for it to fly, and why they are equipped with fire or another heating sources on board? Charles' law is the answer! Whenever the air is heated, its volume increases. As a result, the same amount (mass) of gas occupies a greater space, which means that the density decreases. The buoyancy of the surrounding air does the rest of the job, and so the balloon begins to float. The steering at any given direction is probably a different story, but the general concept of the up and down movement can be explained with Charles' law.

• Liquid nitrogen experiments - have you ever seen an experiment where a ball or balloon is put inside the container filled with liquid nitrogen, and then moved outside? Firstly, it shrinks no matter how big it was at the beginning. Then, after it is freed, it comes back to its initial state. Once again, whenever the temperature changes, so does the volume.

• Thermometer - as shown in the previous section, it is possible to construct a device which measures temperature based on Charles' law. Although we have to be aware of its limitations, which are basically the objects tensile strength and resistance to high temperatures, we can invent an original device that works perfectly to suit our needs. Whenever you are uncertain about the outcome, check this Charles' law calculator to find the answer.

## Other thermodynamic processes

Charles' law, together with Boyle's law and Gay-Lussac's law, are among the fundamental laws which describe the vast majority of thermodynamic processes. We have gathered all of the basic gas transitions in our thermodynamic processes calculator, where you can evaluate not only the final temperature, pressure, or volume, but also the internal energy change or work done by gas.

Wojciech Sas, PhD candidate
Initial parameters
Initial volume (V₁)
Initial temperature (T₁)
K
Final parameters
Final volume (V₂)
Final temperature (T₂)
K
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