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Welcome to the Greenwood.Net Curiosity Corner

Full to the Brim?

Dec 06, 2018

Curiosity Corner
Dr. Jerry D. Wilson,
Emeritus Professor of Physics
Lander University

Question: Suppose you have an ice cube floating in a glass of water that is full to the brim. What happens when the ice cube melts completely? Is the water level lower, is the glass still full, or does some water spill? (Asked by a curious column reader.)

Reply: This is an old one. I have the question in one of my textbooks, so I better know the answers—which are no, yes, and no. No, the water level doesn't fall; yes, the glass is still full; and no, none of the water spills. Let's take a look at why.

As we know, ice is less dense than water. This is why ice floats in water. Using Archimedes' principle on buoyancy, it can be shown that if the density of an object is less than that of a fluid, then the object will rise and float in the fluid. A fluid is either a liquid or gas—a substance that "flows.” A helium balloon rises because it is less dense than air.

It turns out that the density of ice is about 92% of that of fresh water. Also, we can show with a little math (I'll spare you) that about 92% of the ice cube's volume will be submerged in the water. We see only the "tip of the iceberg,” so to speak. This means that the amount of water displaced by the cube is 92% of its volume. (Imagine picking up the ice cube and that its "hole" in the water remains. The volume of this hole is 92% of that of the ice cube.)

So, when the ice cube melts completely, how much or what is the volume of the resulting water? Well, since the density of ice is 92% of that of water, the volume of the water in the ice cube is 92% of the volume of the ice cube -- which just fills the "hole" and keeps the glass full to brim.

That was a short one, so here is some trivia I hope you find interesting:
• What's the hottest thing in your home? Probably an operating incandescent light bulb filament. A 60-W bulb tungsten filament has a temperature of approximately 4350 degrees Fahrenheit (or 2400 degrees Celsius). That is, unless you’ve gone mod and use energy-saving LED bulbs—the heat sinks in these are only up to 212 F (100 C).
• What you always wanted to know. About 75 percent of our belches come from swallowing air. Gas from bacterial and chemical actions (like after a good meal), along with carbonated drinks, account for the rest. We don't think much about "swallowing" air, but as we breathe, air is swallowed into the stomach where about a quart per hour is dissolved. If we get too much air such that it can't be all dissolved, relief is usually in the form of a burp or belches (eructation, if you want to be technical). More air is taken in when you are excited and breathe rapidly, or when chewing gum. In the latter case, swallowing excess saliva gives an extra gulp of air too. Although a natural process, we tend to avoid burping in public. However, if you dine in the Middle East, a hearty burp is the courteous response signaling you enjoyed the meal. But around here, you might want to say "excuse me. I'm sorry to have eructated."
• Invisible persons in movies must be blind. The reasoning goes as follows: if truly invisible, all of the incident light would pass through the person. That is, to be perfectly invisible or transparent, no light could be absorbed or reflected. However, for the invisible person to see, light would have to be absorbed by the eyes. This would allow old "see-trough’s" position to be detected. Hence, a truly invisible person must be blind or can't see. Think about it.

C.P.S. (Curious Postscript): In serving on a jury for a serious case, to acquit, the accused must be found innocent beyond the shadow of a doubt. Guess I can’t serve on such a jury—I’ve never seen a doubt’s shadow.

Curious about something? Send your questions to Dr. Jerry D. Wilson, College of Science and Mathematics, Lander University, Greenwood, SC 29649, or email jerry@curiosity-corner.net. Selected questions will appear in the Curiosity Corner. For Curiosity Corner background, go to www.curiosity-corner.net.

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