# Gay Lussac’s Law, [ formula] Gay Lussac’s Gas Law

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The thermal expansion of gases is quite large. Comparing solids and liquids, when some external pressure is applied, the volume of a gas changes appreciably. While the variation in the volume of solids and liquids is negligibly small and can be ignored for practical purposes.

In order to describe a gas, we require three quantities namely

• Pressure
• Volume and
• Temperature

When any one of these variables changes, the others are bound to undergo variations. We shall study the relationship between any two variables when the third is kept constant.

## Gay Lussac’s Gas Law

For a gas, temperature and pressure are directly proportional. When you keep everything else constant,

• As the temperature of a gas goes up, its pressure goes up.
• As the temperature of a gas goes down, its pressure goes down.

If you heat up a gas, the gas particles move faster. If the gas is in a solid container, with a fixed volume, this means that the faster the gas particles move, the more times per second they collide with the sides of the container. That registers as increased pressure.

The converse is also true – if you cool down this container of gas, that means the gas particles are moving more slowly. So there will be fewer collisions with the sides of the container per second, which means lower pressure.

## Gay Lussac’s Law Formula

Joseph Louis Gay-Lussac shares credit with Guillaume Amontons for establishing a Gas Law describing the relationship between temperature and pressure.

Gay Lussac experimentally studied the variation of pressure of a gas with temperature. According to Gay Lussac, the pressure of a given mass of a gas decreases or increases by a constant fraction of its pressure at 00 Celsius for every 10 degree Celsius fall or rise in temperature, provided its volume remains constant.

In Simple Words,

Gay-Lussac’s Law says that when the volume and amount of gas is constant, pressure and temperature are directly proportional.

P ∝ T

We can write this mathematically as

P = kT

• where P = pressure,
• T = temperature in Kelvin,
• and k = is a proportionality constant.

We can rearrange this equation. So, it reads

P/T = k, or the ratio of pressure to temperature is a constant, k.

Very often, Gay-Lussac’s law is used to compare two situations, a “before” and an “after.” In that case, you can say

P1 / T1 = k, and P2 / T2 = k,

So you can write Gay-Lussac’s law as

P1 / T1 = P2/ T2.

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