# Gay-Lussac's Law Calculator

Created by Davide Borchia
Last updated: Aug 24, 2022

Learn one of the troika of gas laws with our Gay-Lussac's law calculator. Keep reading this article to learn what is Gay-Lussac's law, its formula for the pressure and temperature relationship, and much more. You will be surprised to know that behind many mundane phenomena, we can see the trace of Gay-Lussac's law!

## What is Gay-Lussac's law?

Gay-Lussac's law is a simple thermodynamic formula relating temperature and pressure of a gas at the beginning and end of an isochoric process.

For isochore, we mean a process conducted at a constant volume: we can reach this condition by performing the transformation in a rigid container resistant to deformation. Knowing this, you won't be surprised to learn that Gay-Lussac's law is one of the easiest to prove experimentally.

🙋 The other two thermodynamic laws for transformations in gases are the Boyle's law and the Charles' law. Together with Gay-Lussac's law, they define the combined gas law.

You can easily imagine the consequences of such a process if you consider the microscopic nature of gases: a bunch of molecules free to move, collide, and bounce in a container.

If you increase the temperature, you give energy to the molecules, that in turn get more agitated. The number — and strength — of the collisions on the walls of the container increases.

🙋 On a human scale, pressure is the effect of weight over a surface. When working with fluids — in particular gases — pressure becomes a matter of impact forces: the small molecules hit the walls of the container, thus imparting a negligible force toward the outside. Multiply the collisions by billions, billions of billions, and you get a noticeable pressure.

The collision's change in number and intensity upon an increase in temperature equals an increase in pressure. The same holds in reverse: cool the container, and you will "calm" the molecules and, in turn, reduce the pressure.

Before exploring the consequences of the relationship between pressure and temperature, we need to learn Gay-Lussac's law equation.

## Changing pressure and temperature in a formula: calculating the Gay-Lussac's law.

You already know a verbal explanation of Gay-Lussac's law: let's see how this translates in maths!

What we learned is that pressure and temperature are directly proportional:

$p\propto T$

Even better: they are related by a constant:

$p = k\cdot T$

💡 Use our pressure converter and temperature converter to switch between measurement units quickly.

And, if you want to keep all the state variables on the same side, write:

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

We admit it; this equation is not much useful. To exploit the potential of Gay-Lussac's formula for temperature and pressure fully, we need to consider a process, a transformation of the gas.

🙋 We calculate the value of the constant $k$ in our Gay-Lussac's law calculator: click on advanced to see it!

Say that we start from an initial state defined by:

• $T_1$ — Initial temperature;
• $p_1$ — Initial pressure; and
• $V$ — Volume of the container.

And we reach a final state defined by the following set of variables:

• $T_2$ — Final temperature;
• $p_2$ — Final pressure; and
• $V$ — Volume of the container.

✅ The volume doesn't change in an isochoric transformation!

If one of the four variables (excluding the volume) is missing, we can calculate it: Gay-Lussac's law allows us to set up the following equality:

$\frac{p_1}{T_1}=\frac{p_2}{T_2}$

From which, you can quickly isolate the required variable.

## The consequences of Gay-Lussac's law

The temperature and pressure law appears many times, often unnoticed, in our daily lives. Let's see some examples of situations where the equation for Gay-Lussac's law explains an observable behavior.

1. Inflating your bicycle tires: put a bit of effort into the task, then touch the pump rubber tube. It will be noticeably hotter. Gay-Lussac's law formula tells us that the temperature raises in front of an increase in pressure!
2. Exploding soda cans: leave a can of a sparkling beverage in your car during the summer, then dare yourself to open it. You know what happens, but why? An increase in temperature, this time, caused an increase in pressure.
3. Pressure cookers: in such a piece of kitchenware, the fixed volume of the pot gives us a perfect environment to test Gay-Lussac's law. We leave the observations to you!
Davide Borchia
Initial parameters
Initial pressure (p₁)
Pa
Initial temperature (T₁)
K
Final parameters
Final pressure (p₂)
Pa
Final temperature (T₂)
K
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