Newton’s Law of Cooling: Find the Optimal Coffee/Cocoa Temperature

Newton’s Law of Cooling is a difficult concept for my students to understand. Exponential Growth and Decay is one thing, but Newton’s Law steps it up a notch. Therefore, I developed this short lab to use in class to help the students get a hands-on experience with it.

To complete this lab, you need a few materials:

Hot water to represent the coffee (I have a Keurig in my office)

Different types of cups and mugs (we found it interesting to see which insulates best)

Thermometer (one per group is optimal, but sharing can work)

Basic Plan:

Record temperature of the room. Each group gets a mug of hot water and records temperature. Then, they wait about 5 minutes and record temperature again. They will then, complete the math to see when the water would be the optimal temperature to drink. At the end of the resource, when the instructor is ready, they can put in their data and see if they worked it correctly.

I would like to add a check in real time where they watch and see if the water is the temp that it should be after the time determined. But I haven’t done that yet.

I will generally bring some cocoa packets for students to make themselves a cup of cocoa if desired. (I actually don’t drink coffee so cocoa is what I have.)

(I called it “a very scientific lab” with complete tongue-in-cheek as I know there are many variables that are not controlled.)

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Posted on February 07, 2023

This is such an interesting lab idea, especially in the winter when your coffee seems to go cold before you can have a chance to drink it! I would love to try this in our classroom which has a lot of drafty windows.

Posted on February 08, 2023

Drafty Room: That would be awesome to use as a comparison as well. We all know that the coffee would cool off faster in a cooler environment but quantifying it with math would be fun!

Posted on February 07, 2023

This lab a great example of an opportunity for real-world engagement. Your Numbers file will be an asset for science and math teachers- thank you for including it. I especially like the call outs to taking this lab further by testing different types of mugs. Do I sense a field trip to some local coffee shops in the future? ☕️

Posted on February 08, 2023

Field Trip! Double yes! In one of my other classes, we take a field trip to Dollywood in Pigeon Forge, TN but why didn’t I think of a coffee shop one? In this age of “place-based learning” and “experiential learning,” it is a definite possibility.

Posted on February 07, 2023

Thank you for sharing such a beautifully designed and functional resource with the community. I’ll admit that I’m not a math person so much of this is beyond my comprehension at the moment, but the design and implementation is stellar. And the bonus of a nice cup of cocoa is a great reward for “very scientific” research.

Posted on February 08, 2023

Wonderful use of the Numbers app here!! Making the math interesting will be memorable for your students!

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