Gay-Lussac’s Law is an ideal gas law 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.