Air Pressure Curriculum

Section 3—Lesson 6: Applying Relational Causality to Reasoning About Boyle's Law

Background Information

The Relationship Between Pressure and Volume (at a Constant Temperature)

Understanding pressure-related phenomena involves being aware of different variables and the relationships between them, and reasoning about these variables systematically. Scientists analyze the behavior of a system to see what rules govern its behavior. They have discovered several laws that nature consistently follows in relation to air pressure. One such law is explored in this lesson. Boyle's Law states that at constant temperature (T), the pressure (P) times the volume (V) of an enclosed gas remains constant. In formulaic terms:
PV = k, where k equals some constant value and T is unchanging. Thus, when one increases, the other decreases. A relational causal model nicely demonstrates this. According to Boyle's Law, if the volume increases then the air pressure should decrease to maintain the constant value, k. Let's look at the relationship between force and area more closely. Remember that

If the original force is 4 and the area is 2, then the air pressure is 2 (4/2 = 2). We know that if the volume of an enclosed gas increases, then the area must also increase (for example, to 4). Therefore the air pressure does indeed decrease, to 1 (4/4 = 1), when the volume increases.

Using a Syringe to Demonstrate Boyle's Law

Boyle's Law can be demonstrated with a syringe, the device with a plunger and a barrel to which doctors attach a needle to draw blood samples or give injections. When the plunger is drawn back on the syringe, the volume inside the barrel increases. This decreases the pressure of fluids (such as air or liquids) on the inside of the syringe. The atmospheric pressure outside of the syringe remains unchanged and therefore is greater. The pressure differential that is created forces fluid to enter the syringe. Pushing in the plunger of the syringe decreases the volume inside the barrel, thus increasing the inside pressure. This makes the internal pressure greater than the outside atmospheric pressure. The pressure differential pushes fluids out of the syringe. However, if you hold one of the variables (such as force) constant, you can experience Boyle's Law first-hand. If you cover the opening of the syringe with your finger and then pull the plunger back, the molecules in the fluid inside the syringe spread out to fill the available space. To accommodate the increase in volume, pressure decreases proportionally, and you can feel your finger being "pulled" into the syringe a bit. Conversely, if you draw back the plunger, then cover the opening with your finger, and depress the plunger, the same amount of fluid must fit in a smaller space. Therefore the molecules are pushed closer together, the pressure increases to accommodate the decrease in volume, and you feel the resulting "push" on your finger.

Boyle's Law is in Action Around Us Everyday

There are many examples of Boyle's Law in action around us everyday. For instance, if we step on an inflated balloon or push in on a bubble in a piece of bubble wrap, we decrease the volume and thus increase the pressure inside until it is too great for the outer membrane, and the balloon or bubble pops! When we pump up a bicycle tire, we force air into the tire and the volume of the tire increases to accommodate the additional air without increasing the pressure (until the tire cannot expand any farther and then the pressure increases). Every time we take a breath, the muscle located just below the lungs (called the diaphragm) moves downward, increasing the volume in the lungs. This results in decreased air pressure inside the lungs relative to the atmospheric pressure, which forces outside air into the lungs. Exhaling moves the diaphragm upward, decreasing the volume of the lungs and correspondingly increasing the air pressure inside the lungs as compared to the air pressure outside the lungs. This imbalance in pressure pushes waste gases from respiration out of the lungs. In order to avoid being eaten, a Puffer Fish takes on water (or sometimes air), which increases its volume to maintain a constant pressure, despite the added fluid. If you begin to fill your cheeks with air, your cheeks will expand until they have as much volume as they can accommodate. If you continue to add air beyond this point, you will feel increased pressure. As these examples illustrate, Boyle's Law explains many everyday phenomena. Try to come up with a few examples of your own.