# Ideal gas law

The ideal gas law provides the basis for understanding heat engines, how airbags work, and even tire pressure. The principle equation for the ideal gas law is:[1]

${\displaystyle pV=nRT}$

where:

• ${\displaystyle p}$ is pressure
• ${\displaystyle V}$ is volume
• ${\displaystyle n}$ is the number of moles of gas
• ${\displaystyle T}$ is temperature (measured in kelvin)
• ${\displaystyle R}$ is the ideal gas constant

The value of R depends on the units used. It can also be written as ${\displaystyle pV=Nk_{B}T}$ where N is the number of molecules and ${\displaystyle k_{B}}$ is Boltzmann's constant, with the rest of the variables being the same.

The ideal gas law allows us to determine what will happen to a contained system with an ideal gas inside, based on these different variables. An ideal gas is one that never condenses regardless of the various changes its state variables (pressure, volume, temperature) undergo. For example, if the volume of the system is increased, and all other variables are left alone, the pressure will automatically decrease to compensate for the increase in volume. Conversely, if heat is added to a system, both its volume and pressure will increase to compensate. This latter relationship is the basis for heat engines. For a deeper treatment of the ideal gas law please see hyperphysics, for an extensive treatment please see the UC Davis's chem wiki.

For more information on the assumptions behind the ideal gas law, visit the page on ideal gas approximations.

## How an Airbag Works

Airbags inflate quickly in the case of an accident and reduce injuries. The ideal gas law says that rapidly changing the number of particles (${\displaystyle n}$ or ${\displaystyle N}$) make ${\displaystyle p}$ and ${\displaystyle V}$ increase rapidly.[2]

Oftentimes, physics and chemistry's applications seem quite distant. Here's an example of how these sciences can save a life during a car crash.

Vehicle airbags work using the ideal gas law. By reacting Sodium Azide, ${\displaystyle {\ce {NaN_3}}}$, with excess heat, a large amount of Nitrogen gas (${\displaystyle {\ce {N_2}}}$) is created. The balanced chemical formula for this is ${\displaystyle 2NaN_{3}+heat\Rightarrow 2Na_{+}3N_{2}}$. How does this pertain to the ideal gas law? If you recall, in the ideal gas equation, ${\displaystyle n}$ is equal to the number of moles (a unit of amount) of gas in the system. Before the reaction, the sodium azide is a solid, so there is no gas in the system. By reacting the sodium azide to create nitrogen gas, several moles of gas are added to the system. The ideal gas law says the two sides of the ${\displaystyle pV=nRT}$ equation have to balance; adding moles of nitrogen gas forces the volume of the system to increase dramatically. This inflates the airbag in between 20-40 milliseconds, giving it time to begin deflating before a driver's head hits it. This disperses the force, dramatically improving the chances of avoiding serious injury.[3]

## PhET: States of Matter

The University of Colorado has graciously allowed us to use the following Phet simulation. Explore the simulation to see how particles moving around in a gas lead to various gas properties: