 # Gay Lussac's Law

We have already talked about ideal gas law in one of our other articles. Ideal gas law is the combination of following four laws –

• Boyle’s Law

• Charles's Law

• Gay Lussac’s Law

We have explained Boyle’s Law, Charle’s Law and Avogadro’s law in separate articles. So, in this article we are going to discuss Gay Lussac’s Law in detail.

We have three variables to study gases which are temperature, volume and pressure. In Boyle’s law, temperature remained constant while in Charle’s law pressure remained constant. In Gay Lussac’s Law volume is kept constant. It defines the relation between temperature and pressure for a gas when it is kept under fixed volume.

### What is Gay Lussac’s Law?

Gay Lussac’s Law states that the pressure of a given mass of a gas varies directly with absolute temperature of the gas when the volume is kept constant. In other words, we can say that at constant volume for a given mass of a gas pressure is directly proportional to temperature. It means when temperature will increase, pressure will also increase. It can be expressed as follows –

P ∝ T                (when V = constant)

On removing proportionality –

P = kT -----------(1)

Where P = pressure exerted by the gas

K = constant

T = absolute temperature of the gas

Ideal Gas Equation –

PV = nRT ----------(2)

On keeping the value of P from equation (1) to (2) –

kTV = nRT

k = nR/V

k ∝ 1/V -------------(3)

From equation (3), it means when volume will increase k will decrease.

### Gay Lussac’s Law Graph

Mathematical formula or expression for Gay Lussac’s law can be written as –

P = kT

Now on comparing the above equation with Y = mX, we get Y = P, m = k and X = T so it can be illustrated by graph as given below – image will be uploaded soon.

Blue line or slope in the above graph represents k which is inversely proportional to volume (from equation 3). So, if we increase the volume, the slope will decrease. If V4>V3>V2>V1 then for all these volumes graph between pressure and temperature can be represented as given below – image will be uploaded soon.

### Gay Lussac’s Law of Gaseous Volumes

Law of Gaseous Volumes was proposed by Joseph Louis Gay-Lussac in 1808. According to this law when measured at the same temperature and pressure, the ratio of the volumes of reacting gases are small whole numbers. This can be considered as a different form of law of definite proportions. As this law is with respect to volume while law of definite proportion is with respect to mass.

Example - Images will be uploaded soon.

If 200ml of hydrogen is reacting with 100ml of oxygen then by using Gay Lussac’s law we can calculate how much amount of water(gas) will form. But all should be in gaseous form as Gay lussac’s law is applicable on gases only. If 200ml of hydrogen is reacting with 100ml of oxygen then according to the above equation 200ml of water (gas) will be produced.

This was a brief on Gay Lussac’s Law, if you are looking for various numerical questions based on the law then log on to Vedantu website or download Vedantu learning app. By doing so you can get access to detailed study notes, revision notes, NCERT Solutions, mock tests and much more.