Have you ever burned your tongue when taking a big gulp of that hot drink you just got? This is something that almost everyone has experienced. This would be a relatable activity for students to participate in to determine how long it takes for a hot drink to cool down using the Vernier equipment and software.
Newton’s Law of cooling gives a model, which states that the temperature difference (Tdiff) between a hot object and its surroundings decreases exponentially with time. In the model T0 is the initial temperature and k is a positive constant.
Tdiff = T0 e-kt
In this activity, we will use a Vernier temperature probe to collect data as the hot water that the probe is placed in cools. This activity is applicable because after collecting the data, you can find the line of best fit for the data. By completing this activity, students will be able to see that modeling using regression lines of data is applicable to everyday events.
Objectives of this lesson:
- Record temperature versus time cooling data
- Model cooling data with an exponential function.
Equipment needed:
- EasyTemp or Go!Temp or Temperature Probe and data-collection software
- TI-Nspire handheld or computers and TI-Nspire software
- Hot water
Content standards:
CCSS.MATH.CONTENT.HSF.IF.C.8.B
Use the properties of exponents to interpret expressions for exponential functions.
CCSS.MATH.CONTENT.HSF.LE.A.2
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs.
CCSS.MATH.CONTENT.HSA.CED.A.1
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
The Activity is from Vernier’s website: Chill Out Activity