Vernier Software & Technology

Mix It Up - Mixing Liquids of Different Temperatures

Introduction

Suppose that a hot drink and a cold drink are mixed together and you would like to predict the temperature of the mixture. To do this, you need to know the temperatures of the drinks before they are mixed, T1 and T2, and the volumes of each used in the mixture, V1 and V2. A visual representation of the problem is shown below, where Tm represents the temperature of the mixture:

${T_1}{V_1} + {T_2}{V_2} = {T_m}\left( {{V_1} + {V_2}} \right)$

In this activity you will use the concepts described above to predict the resulting temperature when two solutions of different temperatures are mixed. The data needed to perform these calculations will be collected using a pair of Temperature Probes.

Objectives

• Record temperatures of water samples before and after mixing.
• Compare the mixing temperatures to a linear prediction.

Sensors and Equipment

This experiment features the following Vernier sensors and equipment.

Option 2

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

See other experiments from the lab book.

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

Experiment 7 from Real-World Math Made Easy Lab Book

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.