Under Pressure - The Inverse Relationship between Pressure and Volume

Introduction

Let’s take a sample of air in a closed container, and keep it at room temperature. If you change the volume of the container, what will happen to the air pressure inside? You can feel this by squeezing a small balloon in your hand. As the balloon gets smaller, you have to push harder. That is, as the volume decreases, the pressure increases. Two quantities that change in this way could be inversely related. If pressure and volume are inversely related, even if both quantities change, then their product stays the same.

Suppose that x and y represent the quantities that are inversely related. Then

where k is a constant in both equations. Maybe you can think of some other quantities that also behave this way. For air and other gases, this relation has a name: Boyle’s law.

In this activity, you will use a pressure sensor to investigate the relationship between pressure and volume for air contained within a closed syringe.

Objectives

• Record pressure versus volume data for a sample of air.
• Fit an inverse function model to the data.
• Use the table calculation feature of the TI graphing calculator.
• Re-plot the data using linearization.