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 the following four laws –

• Boyle’s Law 

• Charles's Law 

• Avogadro’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, the temperature remained constant while in Charle’s law pressure remained constant. In Gay Lussac’s Law volume is kept constant. It defines the relationship between temperature and pressure for gas when it is kept under fixed volume. 

What is Gay Lussac’s Law?

Gay-Lussac's is defined as the pressure of a given mass of gas varies directly with the absolute temperature of the gas when the volume is kept constant. Mathematically, it can be written as P/T=k. It is a special case of the ideal gas law.

Vedantu’s website contains separate articles and pdfs on the other three ideal gas laws that are Boyle’s law, Charles’s law and Avogadro’s law. This article is mainly concerned with the Study of gay lussac’s law.

The three elements that help to study gases are temperature, volume and pressure. While studying gay lussac’s law volume is kept constant, the temperature remains constant in Boyle’s law and pressure remains constant in Charles law. Gay lussac’s law defines the relationship between temperature and pressure of a gas when kept in a fixed volume.

An example of gay lussac’s law can be seen in -The propane tanks that we use for barbeque grills. In order to keep a measure of the amount of gas that is left in the tank, people use gauges that measure the pressure in the tank to keep a check on the amount of gas left. The gauge registers a higher pressure when the air temperature is hot. Therefore the air temperature has to be taken into account before refilling the propane tank.

Gay lussac’s law is named after the French chemist who discovered the relationship between the pressure of a gas and its absolute temperature. His name was Joseph gay lussac (1778-1850).

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 a graph as given below – the image will be uploaded soon.

The 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 graphs between pressure and temperature can be represented as given below – the 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 the law of definite proportions. 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 brief on Gay Lussac’s Law, if you are looking for various numerical questions based on the law then log on to the Vedantu website or download the Vedantu learning app. By doing so you can get access to detailed study notes, revision notes, NCERT Solutions, mock tests and much more.