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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]}
where:
The value of R depends on the units used. It can also be written as [math]pV = Nk_B T[/math] where N is the number of molecules and [math]k_B[/math] is Boltzmann's constant, with the rest of the variables being the same.
The ideal gas law allows for 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.
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, [math]\ce{NaN_3}[/math], with excess heat, a large amount of Nitrogen gas ([math]\ce{N_2}[/math]) is created. The balanced chemical formula for this is [math]2NaN_3 + heat \Rightarrow 2Na_ + 3N_2[/math]. How does this pertain to the ideal gas law? If you recall, in the ideal gas equation, [math]n[/math] 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 [math]pV = nRT[/math] equation have to balance; adding moles of nitrogen gas forces the volume of the system to increase dramatically. This inflates the airbag in between 2040 milliseconds, giving it time to begin deflating before a driver's head hits it. This disperses the force, dramatically improving chances of avoiding serious injury.^{[3]}
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: