The Ideal Gas Law was discovered in 1834 by Benoit Paul Emile Clapeyron--you may have heard of the Clausius-Clapeyron equation--and is kind of a big deal. It allows us to calculate a lot of information about a gas and how it will behave, so it is an important concept in thermodynamics. However, it has limitations; there are really no such things as ideal gasses, for example, and it only holds under certain conditions. Still, many gasses are close enough to ideal that this law is a valuable predictive tool.
By analyzing questions, you can see patterns emerge, patterns that will help you answer questions. Qwiz5 is all about those patterns. In each installment of Qwiz5, we take an answer line and look at its five most common clues. Here we explore five clues that will help you answer a tossup on the Ideal Gas Law.
PV=nRT
According to the Ideal Gas Law, the product of the pressure and volume of an ideal gas is proportional to the number of moles of the gas and its absolute temperature. This relationship is expressed as PV=nRT, where P, V, and T are pressure, volume, and temperature. R is the ideal gas constant, and n is the number of moles of gas present.
The ideal gas constant (roughly 8.134 joules per mole kelvin) is actually also equivalent to the Boltzmann constant (one of the seven “defining constants” in the SI unit system), but the two are expressed in different units. The ideal gas constant R is also equal to the product of the Avogadro constant and Boltzmann’s constant.
The Ideal Gas Law combines several other laws: Boyle’s Law, Charles’ Law, Avogadro’s Law, and Gay-Lussac’s Law.
BOYLE’S LAW
Boyle’s Law, formulated by Robert Boyle, states that the pressure of an ideal gas is inversely proportional to the volume of the gas. It also shows the product of the pressure and volume of a gas is a constant, or PV=k. Boyle’s law can be used to calculate the Carnot cycle.
CHARLES’ LAW
Charles’ Law was discovered by Jacques Charles, but was first presented publicly by John Dalton. It states that the volume of a gas divided by its temperature is a constant, or V=kT. In other words, if pressure is held constant, a gas will expand as temperature increases, and will shrink in volume as temperature drops.
GAY-LUSSAC’S LAW
Joseph Louis Gay-Lussac, who was also notable for establishing that water is composed of two parts hydrogen to one part oxygen, established the relationship between pressure of a gas and its temperature. In his equation, P/T=k, or the pressure of the gas is directly proportional to pressure. This law is also sometimes known as Amonton’s Law.
AVOGADRO’S LAW
Amadeo Avogadro, the namesake of Avogadro’s number, theorized that if temperature, pressure, and volume of two samples of an ideal gas are equal, each sample will have the same number of molecules of gas.
All of these laws can be connected algebraically through the relationship PV/NT = KB, where N is the number of particles of a gas and KB is Boltzmann’s constant. If you’re confused, though, don’t worry!
Just remember your ABCs:
Avogadro is All (Volume,Temperature and Pressure)
Boyle is Pressure and Volume
Charles is Temperature and Volume
Guy-Lussac is the leftover, Pressure and Temperature.
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Quizbowl is about learning, not rote memorization, so we encourage you to use this as a springboard for further reading rather than as an endpoint. Here are a few things to check out:
* Ready to go a little deeper into gas laws, and look at things like Dalton’s Law of partial pressure? Khan Academy has a full unit on the Ideal Gas Law that will get you to the next level.
* Fun Fact--did you know that gas balloons are also occasionally known as Charlières, after their inventor, Jacques Charles? Check out Jacques’ daredevil side courtesy of the British Balloon Museum.
* In the midst of the "Deflategate" scandal, a Tom Brady fan gave a shoutout to the Ideal Gas Law through a custom-made jersey.
* Don’t confuse Boltzmann’s constant with the Stefan-Boltzmann constant! The latter has to do with black body radiation, and you can learn more about it here on Wikipedia.
* Are you a visual learner? YouCanScienceIt has a short video with five examples of how the Ideal Gas Law works in practice.
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