# Gay-Lussac's Law Calculator

Created by Wojciech Sas, PhD
Reviewed by Bogna Szyk and Jack Bowater
Last updated: Dec 04, 2023

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 gas law to hold true, the gas container must be built 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.

🙋 Want to know how ideal gas behaves? Check out our ideal gas law calculator.

## 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!

2. 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.

Are you interested in learning more about pressure? Check out our pressure calculator.

## 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 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 doing 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 decrease.

## FAQ

### What is Gay-Lussac's law?

Gay-Lussac's law is a relationship between pressure and temperature in ideal gases and constant volume. Alongside Boyle's and Charles's laws, it constitutes one of the components of the combined gas law.

Gay-Lussac's law states that the ratio between pressure and temperature is constant as long as the volume doesn't change:

p/T = k

### How do I calculate Gay-Lussac's law?

To calculate Gay-Lussac's law, you need to follow some easy steps:

1. In a rigid container, measure the pressure p₁ and the temperature T₁ of your gas.

2. Compute the ratio between pressure and temperature: k = p₁/T₁.

3. Multiplying any value of temperature by k, you can find the corresponding pressure in the same container: p₂ = k × T₂.

4. You can find the temperature by dividing each value of pressure by k: T₂ = p₂/k.

### Where can I observe Gay-Lussac's law?

You can observe Gay-Lussac's law in many everyday life objects:

• Pressure cookers: by sealing the lid, the volume remains constant; the increased pressure and temperature facilitate the cooking process.
• Aerosol cans: when you empty the can, you reduce the pressure inside it. Gay-Lussac's law tells us that the temperature reduces too, and this is what you can observe.
• Cans exploding in a fire do this due to increased pressure caused by the high temperature.

### What temperature will my pressure cooker reach if its maximum pressure is 0.2 bar?

You can reach a temperature of about 175 °C. To calculate this value, follow these steps:

1. Calculate the Gay-Lussac's law constant at atmospheric pressure and the boiling point of water (100 °C or 373 K):

k = p₁/T₁ = 0.99 bar/373 K = 0.00265 bar/K

2. Divide the pressure your cooker can reach by k:

T₂ = p₂/k = (0.99 + 0.2) bar/0.00265 bar/K = 449 K (175 ºC)

3. Notice that the excess temperature was:

**ΔT = T₂ - T₁ = 175 ºC - 100 ºC = 75 ºC **

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