# Question #779c9

Feb 17, 2014

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:

$\frac{{P}_{1}}{{T}_{1}}$ = $\frac{{P}_{2}}{{T}_{2}}$

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.

$\frac{1 a t m}{273 K} = \frac{P}{546 K}$

$\frac{546 a t m K}{273 K} = P$

P = 2 atm

Doubling the temperature, likewise doubled the pressure.