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# What is Gay-Lussac's law?

Gay-Lussac’s Law is an where at constant volume, the pressure of an ideal gas is directly proportional to its absolute temperature. In other words, Gay-Lussac's Law states that the pressure of a fixed amount of gas at fixed volume is directly proportional to its temperature in kelvins.

Simplified, this means that if you increase the temperature of a gas, the pressure rises proportionally. Pressure and temperature will both increase or decrease simultaneously as long as the volume is held constant.

The law has a simple mathematical form if the temperature is measured on an absolute scale, such as in kelvins. The Gay-Lussac’s Law is expressed as:

##(P_1)/(T_1)## = ##(P_2)/(T_2)##

Where ##P_1## stands for the initial pressure of the gas, ##T_1## stands for the initial temperature, ##P_2## stands for the final pressure of the gas, and ##T_2## stands for the final temperature.

This law holds true because temperature is a measure of the average kinetic energy of a substance; when the kinetic energy of a gas increases, its particles collide with the container walls more rapidly and exert more pressure.

Take a sample of gas at STP 1 atm and 273 K and double the temperature.

##(1 atm)/(273 K) = P/(546 K)##

##(546 atm K)/(273 K) = P##

P = 2 atm

Doubling the temperature, likewise doubled the pressure.