# Gay-Lussac's Law Calculator

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

This Gay-Lussac's law calculator provides you with information about the basic gas parameters during an isochoric transition. In the text, you will find a definition of Gay-Lussac's law, some equivalent Gay-Lussac's law formulas, and a few computational examples so you know you fully understand what's going on. Did you know that Gay-Lussac's gas law can be applied to your everyday activities? Check out some of the most interesting ones!

## Gay-Lussac's law definition

Gay-Lussac's law (also known as the pressure law) describes the relationship between the pressure and temperature of a gas when there is a constant amount of gas in a closed and rigid container. The law states that the absolute pressure is directly proportional to the temperature.

For Gay-Lussac's law to hold true, the gas container must be build in such a way that the volume of the gas remains constant under any condition. In other words, Gay-Lussac's law tells us about the behavior of an ideal gas during an isochoric (constant-volume) process.

## Gay-Lussac's law formula Using the definition above, one form of the Gay-Lussac's law formula can be written in the following way:

`p₁ / T₁ = p₂ / T₂`,

where `p₁` and `T₁` are initial pressure and temperature, respectively. Similarly, `p₂` and `T₂` are the final values of these gas parameters.

However, this is not the only form of the equation. For example, if you wanted to check the relationship between the initial and the final pressure, the formula would become:

`p₁ / p₂ = T₁ / T₂`.

As we can see, the ratio of the initial and final temperatures is proportional to the ratio of the initial and final pressures. With this Gay-Lussac's law calculator, you can evaluate any one of these four parameters, provided you know the three other parameters. Just insert the three known values, and the last one will be estimated instantly. Moreover, in advanced mode, you can also work out the amount of gas in moles, depending on the volume of the container.

## Gay-Lussac's gas law examples

How about we move on to solve some computational problems?

1. Let's say we have a metal can containing `300 ml` of air in a `20°C` room, and the initial pressure of the gas is `100 kPa` (we can also write `10⁵ Pa` using scientific notation). Then we heat our container so that the temperature reaches `400°C`. Assuming that the can isn't leaking, what is the final value of the pressure inside?
• To start, we need to convert the temperatures into the absolute scale, Kelvin, which is necessary for Gay-Lussac's law: `T₁ = 20°C = 293.15 K`, `T₂ = 400°C = 673.15 K`.
• The next step is to rearrange Gay-Lussac's law formula to estimate the final pressure: `p₂ = p₁ / T₁ * T₂ = 100 kPa / 293.15 K * 673.15 K = 229.63 kPa`.
• We can also evaluate the amount of gas in moles using the information provided to us in the question: `n = p₁ * V₁ / (R * T₁) = 100 kPa * 300 ml / (8.314 J/(mol*K) * 293.15 K) = 0.0123 mol`. Here `R` is the gas constant.
• You can always check the answer with our Gay-Lussac's law calculator, or simply use it to save time!
1. In this example, we have a rigid box filled with nitrogen, and we know that it is heated to `460 K` while the internal pressure is equal to `1.6 atm`. After some time it is cooled down to the point where the pressure drops to `1 atm`. What is the final temperature?

The answer is relatively easy - just apply Gay-Lussac's law: `T₂ = T₁ * p₂ / p₁ = 460 K * 1 atm / 1.6 atm = 287.5 K`.

Just a small remark concerning the results. We have to be aware that both problems are examples of real gases, whereas all of the formulas are only 100% accurate for ideal ones. However, in such computational problems, the outcome is actually a really good approximation, so, as long as we don't put our gas into some extremal conditions (pressure or temperature), these results can be used.

## Gay-Lussac's law in real life

Can we actually see how Gay-Lussac's law works in our daily life? Take a look at these examples:

• Tire pressure in different seasons - Have you ever inflated a tire during winter, only for it to be overinflated when the weather got warmer? Or inversely, when it was filled during summer, did the pressure decrease when it cooled down? In this case, tires are an example of a closed system, so the higher the temperature, the higher the pressure.

• Lid on a saucepan - At first, it may look pretty obvious, but why does the cover repeatedly jump and rattle around while you are heating your meals in a pot? Increasing the temperature results in higher pressure of the gas (mainly water vapor) inside the saucepan. At some point, the pressure is high enough to lift the lid, and the excess of gas is released, the pressure is leveled, and the whole process starts over again, and again...

• Putting a hot can into cold water - This is a simple way of testing that Gay-Lussac's law is true, if you don't believe us already. Just take an empty metal can of your favorite beverage and safely heat it up. We strongly recommend to do this outside, not at home! After a short time, you can try to plug the hole and then put the can into cold water. If you are successful, the can will shrink, due to the internal temperature dropping also causing the pressure inside to decreases.

## Other thermodynamic processes

Gay-Lussac's gas law, together with Boyle's law and Charles's law, are among the fundamental laws which describe the vast majority of thermodynamic processes. If you are interested in estimating the change in temperature, work done by gas, or simply want to compare the results for different gas types, you can check our thermodynamic processes calculator where we have collected all of the basic gas transitions!

Wojciech Sas, PhD candidate
Initial parameters
Initial pressure (p₁)
Pa
Initial temperature (T₁)
K
Final parameters
Final pressure (p₂)
Pa
Final temperature (T₂)
K
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