Gay Lussac's law explains the relation between Pressure and Temperature of a gas. This is one of the gas laws which would help us understand the relations among pressure , temperature and volume of a sample gas. These sample relations hold approximation for all gases because all gases behave similarly in large conditions since they all have similar wide spread of molecules. The gas laws discovered at the end of 18th century.

Coming to Gay-Lussac's law, which was discovered by Joseph Louis Gay-Lussac in 1809. This states the relationship between pressure and temperature of a gas, when volume of the gas kept constant.

It states that * For a given mass and constant volume of an ideal gas, the pressure exerted on the sides of its container is directly proportional to its absolute temperature. *

i.e.,

PαT

To further equate them, we can use proportionality constant *k.*

\frac{P}{T} = k

So, imagine P_1 and T_1 are the initial pressure and temperatures of an ideal gas for a volume V.

\frac{P_1}{T_1} = k

For the same unchanged volume *V, *let P_2 and T_2 are newer changed values of pressure and temperature of the same gas. Then acc to the law,

\frac{P_2}{T_2} = k .

Equating above two equations, we get

\frac{P_1}{T_1} = \frac{P_2}{T_2} = k

\Rightarrow\ \frac{P_1}{T_1}=\ \frac{P_2}{T_2}.