Gay-Lussac's Law

When you have a can of soda or beer, and you heat it too much by leaving it in your car or out in the sunlight for too long a period of time, you may find an unpleasant surprise when you return to fetch it, as people have found out here and here.  The amount of liquid in the can hasn't grown. Instead, the carbon dioxide inside has been agitated thermally, thus increasing the pressure, and you then have to deal with the messy results of container bursting due to this increase in kinetic energy. Inconvenient incidences of pressurized containers exploding when they are heated may be explained by the Law of Gay-Lussac.

Gay-Lussac's Law is the third and final of the laws leading up to the ideal gas law. The first is Boyle's Law, which gives the relationship between volume and pressure, and the second is Charles' Law, which gives the relationship between volume and temperature. Gay-Lussac's Law has also been referred to as Charles' Law, but they are not the same.

The founder of this particular thermodynamic relation is Joseph Gay-Lussac (1785-1850). He not only rescued Charles' Law from oblivion by duplicating the experiments and publishing the results, but re-created similar conditions to find the connection between pressure and temperature. Gay-Lussac found that for a gas, if the pressure increases, the temperature increases, and if the temperature increases, so does the pressure.

According to Gay-Lussac's Law, at constant volume V, the pressure P is directly proportional  to the temperature T:

1) P _˜ T

or

2) P = kT where k = constant

Rewriting equation 2, we have:

3) P/T = constant

Gay-Lussac's Law is also commonly written as:

4) P₁/T₁ = P₂/T₂

where P₁ and T₁ are the original values of the gas, while P₂ and T₂ represent its final values. In addition to the pressure being constant, the same caveats used in any ideal gas law apply here. These results apply for systems where an equilibrium state has been reached, the gas is not too dense, and P is around atmospheric pressure. Real gases approximate these conditions enough such that the law is applicable in every day life.

So what is the physics behind containers that explode when they are sufficiently heated? When you increase the temperature for a gas where the volume is constant, you also force an increase in its pressure. Heat a container of soda enough, and it will explode as shown here. For this reason, it is unwise to leave a beer keg too long out in the sun or to deliberately heat it. It is an unfortunate fact that exploding beer kegs have actually killed people in mishaps such as this and this. There is also an incident of kegs exploding in the back of a truck. I strongly suspect that thermal agitation was involved there as well, albeit inadvertently.

Image Credits

PT Graph From www.ChemCool.com

Gay-Lussac Stamp From Physics Related Stamps

Physics for Scientists and Engineers by Douglas Giancoli

• Robert Brombach's Demonstrations of the Three Gas Laws
• A Very Cool Interactive Shockwave Simulation for Charles' Law (complete with piston and graph and data table)
• Another Charles' Law Shockwave Simulation
• Excerpts From Gay-Lussac's Original Paper The Expansion of Gases by Heat - notice section 2 where he gives full credit to Jacques Charles