One of the interesting experiments done in 8th grade physical science is a demonstration in which the temperature of a mixture of ice and water is measured, while it is being heated with a Bunsen burner or a hot-plate. Even though substantial energy is being put into the mixture of ice and water, the temperature stays fixed at (approximately) 0 degrees C. What changes, of course, is the amount of ice in the bath. Once all the ice has melted, then the temperature of the water begins to increase.
If you continue to heat it, the temperature of the water will increase in (almost) direct proportion to the amount of energy put into it, until it gets to (approximately) 100 degrees C. At 100 degrees C, the temperature will again hold steady, while the water boils, until it has been completely converted to steam.
The phase change from solid (ice) to liquid (water), and then to gas (steam) requires energy. That energy is well defined, too. The energy difference between liquid and solid is know as the "latent heat of fusion." In order to turn 1 kilogram of ice into 1 kilogram of water requires 333.55 kilojoules of energy.
Suppose you wanted to melt a column of ice 200 feet tall, and 10 feet in diameter. That would be a cylinder with a volume of pi * radius^2 * height = 3.14159 * 25 feet^2 * 200 feet = 15707.95 cubic feet, or (using Google to convert units) 444.8 cubic meters, or 444,800 liters. Ice has a density of about 0.9167 kg / liter, so we're trying to melt 407,748 kg of ice. This will require 407,748 * 333.55 kilojoules of energy, or 1.36 x 10^12 joules. 1 Joule per second is one Watt of Power, so if we were trying to melt this ice in, say 2 weeks = 336 hours = 1,209,600 seconds, we would need to continuously apply (assuming there were no other thermal inputs or outputs to our system) 1.36 x 10^12 joules / 1.2096 x 10^6 seconds = 1.124 x 10^6 watts, or about 1.1 megawatts.
Hmmm. That's a lot of energy to deliver, continuously, for two weeks straight, so it would be really hard to melt a column of ice 200 feet high and 10 feet across. Especially with a gallium arsenide laser. The motivation for this exercise is intentionally left cryptic. But I'm looking at you again, Dan Brown.
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4 comments:
I'm pretty sure it's called "fiction" for a reason. Just sayin'...
Yeah, and that's why I call it a "nit." Still, wouldn't you find it detracted from a story if you were reading a novel about current day police work and they mention in passing how the cops then hopped in their Crown Vic cruiser, and drove across town in 22 seconds at 800 miles an hour? You'd probably think, "What the hell?!? That doesn't make any sense at all!"
But that's exactly what all cop stories are like. I just giggle because I know people believe the inaccuracies. I'm pretty sure that means someone thinks I'm Wonderwoman! And yes, I still watch CSI. I even occasionally catch an episode of Cops (also known as "How NOT to be a Cop"). I think I would be more distracted if things were accurate.
Yeah, okay, I forgot about CSI. But at least they have the excuse of "we're cranking these puppies out every week." Again, I think my major annoyance is just that Brown is so highly regarded for the quality of his research. And yet, when you scratch the surface it kinda falls apart. Oh well. I'll get off it. Probably. Mostly.
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