In order for a hydrogen fuel cell to work, the problems of hydrogen fuel storage must be overcome. By using Charles' Law and Boyle's Law to explain the relationships of gasses to pressure, temperature and volume, a greater understanding of how to store hydrogen can be achieved.
Due to being a gas, hydrogen is hard to contain and has a very low density. In order to store enough hydrogen for the fuel to be effective, fuel tanks become incredibly heavy limiting fuel efficiency. However, lightening the load for fuel efficiency results in not enough hydrogen fuel for effective traveling distance.
Boyle's Law works to describe how to maintain the correct pressure, volume balance within the fuel cell. Boyel's law reads, "The pressure of a given mass of gas is inversely proportional to its volume at a constant temperature." Boyle's law explains that as long as the temperature doesn't change, the more pressure gas is kept under, the smaller volume the gas will take up. Keep the gas under pressure and it will be much more dense. This is essentially what you do when you stuff your sleeping bag into the case. Large sleeping bag is stuffed into a much smaller space, making the sleeping bag more dense. In hydrogen fuel storage, pressurizing the gas causes for dense storage if you can keep the temperature constant.
Where Boyle studied pressure, Charles studied temperature. To quote directly, Charles' law states, "The volume of an ideal gas at constant pressure is directly proportional to the absolute temperature." If the pressure is the same, gas expands as the temperature is increased. This poses 2 problems for hydrogen fuel storage. The first, in order for pressure to say the same as gas expands, the storage would have to expand with it. Without the storage expanding, you would have an expanding gas in a confined space reaching explosive pressures (think hydrogen bomb or the Hindenburg). For this reason, a fuel cell needs to be kept at a constant low temperature in order to keep the gas confined and not to increase the pressure within the fuel cell. If the pressure must remain low, then the temperature must remain low as well. By super cooling the hydrogen, a much more dense state is achieved.
Boyle's law is important to hydrogen fuel cells because it explains how pressurizing the hydrogen can liquefy the gas for maximum storage capacity. Unfortunately, in order to do that, the temperature needs to be kept so low (Charles' Law) it is unrealistic to consider.
Ideal Gas Law
Due to both laws expressing temperature, pressure, and volume they were combined to form an equation called the Ideal Gas Law. By using the Ideal Gas Law, any changes in temperature, pressure, or volume can be balanced by the other forces allowing for stable containment. The Ideal Gas Law is only for ideal situations and does not allow for any outside variables. To use the Ideal Gas Law in real life, a modifier must be added.