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# What if Boyle's Law focused on internal pressure?

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Boyle's law focuses on external pressure. What might be the case if it focuses on the internal pressure? How would this aspect change Boyle's law?

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To start, I will give you the scenario of a balloon filled with gas molecules.

Gas molecules inside a volume (in this instance, a balloon) move around freely and constantly within this given space. As they move, they collide with one another frequently, as well as with the surface of any enclosure there may be. The force of impact against the surface of the enclosure is what is known as gas pressure. The more collisions that there are, the greater the measure of gas pressure. This means that as the size of the enclosure decreases, the pressure will ultimately increase, because the gas molecules are more likely to hit the surface of the enclosure as they move about because the area in which they can move has decreased.

In the case of the balloon, the internal pressure resides within the balloon, which are represented as gas molecules moving within and hitting the inner surface of the balloon, exerting pressure within it. The external pressure resides outside of the balloon, represented by gas (air) on the outside, exerting pressure onto the outside surface of the balloon. The rate by which the outer surface of the balloon is bombarded by air molecules depends on how tightly the gas molecules are packed, which is known as the gas density. Because gas molecules are compressible, gas density will rely upon the force that is used to compress the molecules.

Assuming that our balloon is tight, so that the mass of the air within the balloon remains constant, we can then assume that the gas density of the balloon will vary only with its volume (this is due to the fact that density = mass/volume, thus, if mass is constantly the same, the value of density will change ONLY if the value of the volume changes)

Thus, if we were to squeeze the balloon, we would compress the air within the balloon. This would result in the density increasing inside the balloon (density increases as air is compressed) and the air pressure increasing in the balloon (reduction in balloon space makes it more likely that molecules will more frequently collide within the inner surface). Since density = mass/volume, and the mass stays constant, the increase in density means that the volume of the balloon must decrease (density has an inverse relationship to volume): thus, as pressure goes up; volume ultimately goes down.

According to Boyle's law: at a constant temperature, the volume of a given mass of gas varies inversely with pressure. For two states of pressure (P1, P2) and two corresponding volumes (V1, V2), this is stated mathematically: P1 * V1 = P2 * V2.

This is true when there is external pressure, that is, when we apply force to the outside of the balloon (compress it) which increases density and pressure within the balloon and decreases the volume of the balloon. However, what would happen if there was internal pressure? That is, what if the force came from inside the balloon?

Thinking about it this way, suppose a force within the balloon were to exert itself. If the temperature were to suddenly increase, this would in turn increase the speed of the moving gas molecules moving inside the balloon. This would then result in an increase in the rate at which the gas molecules bombard the inner surface of the balloon (or, an increase in gas pressure). Due to the fact that the balloon is made up of an elastic material, it expands upon this increased force within it, which increases the volume taken up by the same mass of gas. Because mass remains constant, yet the volume of the balloon has increased: density = mass/volume, thus, density must decrease in response to an increase in volume. With internal pressure, we see a very different effect from external pressure, in that pressure and volume BOTH increase (instead of pressure increasing while volume decreases) and density has decreased. There is no longer an inverse relationship between pressure and volume, as there is in Boyle's law, so this aspect would change Boyle's law.

This is why Boyle's law requires that forces, such as temperature, that could affect the internal pressure must remain constant in order for Boyle's law to apply.

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