Comments on: I Have The Coolest Hobbies, Ctd.

By: Naomi

Naomi — Thu, 17 Mar 2011 13:46:51 +0000

Surface Area & Melting with Ice Cubes

http://www.figurethis.org/challenges/c62/challenge.htm

By: dy/dan » Blog Archive » [WCYDWT] Cheese Blocks

dy/dan » Blog Archive » [WCYDWT] Cheese Blocks — Tue, 08 Mar 2011 23:59:06 +0000

[…] model adequately. I can't adequately explain a microwave. This link was extremely helpful (thanks, Jean-Marc!) as was this explanation (thanks, Carmen!) but in my hands this problem verges on pseudocontext […]

By: dy/dan » Blog Archive » I Have The Coolest Hobbies, Ctd.

dy/dan » Blog Archive » I Have The Coolest Hobbies, Ctd. — Tue, 08 Mar 2011 23:56:23 +0000

[…] Feb 27. Liz Clark writes back in, having taken the rotating tray out of the microwave and melted one cube at a time […]

By: Paul Hawking

Paul Hawking — Mon, 28 Feb 2011 01:59:53 +0000

@Geoff: You can make a sphere of ice with a Christmas ornament mold:

http://www.anoccasionalchocolate.com/christmas-ornament-ball-mold.html

http://chemistry.about.com/od/glowinthedarkprojects/a/glowingiceball.htm

Paul Hawking
Blog:
The Challenge of Teaching Math
Latest post:
“Second Draft: Dear Parents Letter”
http://challenge-of-teaching-math.blogspot.com/2011/02/second-draft-dear-parents-letter.html

By: Geoff

Geoff — Mon, 28 Feb 2011 01:15:38 +0000

This also reminds me of the question of “what shape should ice be?” Using either cheese or ice melting, students could investigate various shapes and dimensions.

Spheres should melt the slowest as they have the lowest SA:Volume ratio. Getting a sphere of ice is tricky though. Alton Brown of the Food Network had an episode where he froze water in a balloon to use in a punch bowl.

By: Liz

Liz — Sun, 27 Feb 2011 00:36:31 +0000

I tried the demonstration again putting each cube into the microwave individually. The results agree with Dan’s video.

Small cube begins to melt at 8 seconds and takes 3 seconds to melt.

Medium cube begins to melt at 5 seconds and takes 4 seconds to melt.

Large cube begins to melt at 9 seconds and takes 14 seconds to melt.

The point of my lesson was the surface area to volume ratio, much like the comments on cell biology and baby in the car.

By: Alexandre Owen MuÃ±iz

Alexandre Owen MuÃ±iz — Fri, 25 Feb 2011 22:38:53 +0000

I have a problem with the characterization of that experiment as measuring the speed of light. You’re only measuring the wavelength — you’re relying on the manufacturer to provide you the frequency. But what if they themselves determined the frequency from the wavelength and the speed of light?

By: Carmen Taylor

Carmen Taylor — Fri, 25 Feb 2011 22:32:49 +0000

Hi Dan,

I think this doesn’t conflict with your other data. The way I calculate it, if the 3 cheese blocks here are cubes of side x, then we can calculate a volume/surface area ratio as

V/SA = x^3 / (6x^2) = x/6.

If that’s the case, then the bigger the cube, the faster it heats up relative to how fast it can radiate heat, and so the biggest cheese block should melt first. Isn’t this the result you found?

I posted a model of this under your original data, with a proposed explanation of the reason for the exponential fit. Let me know if I’ve missed something.

By: Maria

Maria — Fri, 25 Feb 2011 15:19:23 +0000

wouldn’t this be a great integrated math/science lesson? knowing the ‘whats’ seeking the ‘whys’?

By: Patti

Patti — Fri, 25 Feb 2011 02:24:13 +0000

From what I have read, it will be important to 1) remove the rotational aspect of the microwave and 2) make sure that each cube of cheese is placed in the same spot of the microwave. This will probably change the data in Dan’s table of melting times, but will it be a significant change?