Vernier Software and Technology
Vernier Software & Technology

Under Pressure - The Inverse Relationship between Pressure and Volume

Figure from experiment 15 from Real-World Math Made Easy

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

xy = k,{\text{   or  }}x = \frac{k}  {y}

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.

Sensors and Equipment

This experiment features the following Vernier sensors and equipment.

Additional Requirements

You may also need an interface and software for data collection. What do I need for data collection?

Standards Correlations

See all standards correlations for Real-World Math Made Easy »

Real-World Math Made Easy

See other experiments from the lab book.

1Walk the Line - Straight Line Distance Graphs
2Making Cents of Math: Linear Relationship between Weight and Quantity
3Pool Plunge - Linear Relationship between Water Depth and Pressure
4Funnel Volumes - Volume and Weight
5Keep It Bottled Up - Rates of Pressure Increase
6Graph It in Pieces: Piecewise Defined Functions
7Mix It Up - Mixing Liquids of Different Temperatures
8Spring Thing - Newton's Second Law
9Stretch It to the Limit - The Linear Force Relation for a Rubber Band
10What Goes Up - Position and Time for a Cart on a Ramp
11That's the Way the Ball Bounces - Height and Time for a Bouncing Ball
12Walk This Way - Definition of Rate
13Velocity Test - Interpreting Graphs
14From Here to There - Applications of the Distance Formula
15Under Pressure - The Inverse Relationship between Pressure and Volume
16Light at A Distance - Distance and Intensity
17Chill Out: How Hot Objects Cool
18Charging Up, Charging Down - Charging a Capacitor
19Bounce Back - The Pattern of Rebound Heights
20Sour Chemistry - The Exponential pH Change
21Stepping to the Greatest Integer: The Greatest Integer Function
22Swinging Ellipses - Plotting an Ellipse
23Crawling Around: Parametric Plots
24Lights Out! - Periodic Phenomena
25Tic, Toc: Pendulum Motion
26Stay Tuned: Sound Waveform Models
27Up And Down: Damped Harmonic Motion
28How Tall? Describing Data with Statistical Plots
29And Now, the Weather - Describing Data with Statistics
30Meet You at the Intersection: Solving a System of Linear Equations
31Titration Curves: An Application of the Logistic Function

Experiment 15 from Real-World Math Made Easy Lab Book

<i>Real-World Math Made Easy</i> book cover

Included in the Lab Book

Vernier lab books include word-processing files of the student instructions, essential teacher information, suggested answers, sample data and graphs, and more.

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