Hatrack River Forum: So* how many ice cubes would it take?

This is topic So* how many ice cubes would it take? in forum Books, Films, Food and Culture at Hatrack River Forum.

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Posted by Narnia (Member # 1071) on :

One of my high school students handed me this flyer today:

quote:
Want it to snow? Here's your chance to MAKE IT HAPPEN!

We're asking everyone to put at least 12 ice cubes outside tonight at 9:30 pm, to increase the possibility of snow. Our theory is that the ice cubes will cool the atmosphere, lower temperatures and increase chances for snow! Wouldn't it be nice to wake up Thursday morning, ready to go to school and take finals, to find out that there's a snow day instead? There's not hurt in trying! Thanks for your help! Sincerely, the ACSS (Association of Concerned Students for Snow)

Everyone's in a flutter because we might get some snow (and if this place burps snow, school gets canceled) and I thought that this little message was hilarious. It's been circulating all over the school and I got to wondering: "Will my ice cubes really help?"

What do you think? I'm sure there is someone smarter than me out there that can say that it's hogwash (which I'm assuming it is) and then can tell us how many ice cubes it really would take to lower the temperature of the atmosphere! [Big Grin]

[ November 30, 2005, 08:30 PM: Message edited by: Narnia ]

Posted by Stan the man (Member # 6249) on :

What? to have enough? Fly to the North Pole and bring an iceberg back with you. That should do it [Smile]

. It is funny that that idea is about. especially with finals coming up.

Posted by James Tiberius Kirk (Member # 2832) on :

One would have to know the temperature of the ice cubes, the temperature of the outside air, the mass of the cubes, and the mass of the outside air. (to calcualate the enthalpy change). You'd also need to know the relative makeup of the air in order to come up with a specific heat for the atmosphere.

But even without all that math, I can confirm for you that it's going to take a lot more ice cubes that an average-sized school can produce.

--j_k

Posted by SteveRogers (Member # 7130) on :

I'd say that all of the ice cubes in your local Wal-Mart would suffice.

Posted by Narnia (Member # 1071) on :

So my two ice trays won't do it?

Dang.

Posted by Teshi (Member # 5024) on :

You have to give them points for trying.

Posted by James Tiberius Kirk (Member # 2832) on :

Mostly cause I'm bored:

I'm using dry air; [0% humidity 1005 j/kg*C] it actually takes more energy to change the temperature of air with H2O in it [100% humidity = 1030 J/kg*C]. I'm also cooling the entire atmosphere, because I don't have a way to isolate the air over the town, and assuming that the atmosphere is a uniform 10 C. (50F) The ice starts off at -18 C (0F)

code:

Mass of atmosphere: 5.1e18 kg
Specific heat of (dry) atmosphere: 1005 J/kg*C
Current temp of atmosphere: 10C
Target temp of atmosphere: 0C
dT_air = -10 C

1005 * 5.1e18 * -10 = -5.1e22 J

which means 5.1 * 10^22 joules of energy must be removed from the air to cool it from 10 C to 0 C.

code:

Specific heat of ice: 4.18 j/g*C
Current temperature of ice: -18 C
Target temperture of ice: 0 C
dT_ice = 18 C

5.1e22 = 4.18 * mass * 18

mass = 6.8e20 g = 6.8e17 kg

So 6.8 * 10^17 kg of water, at -18C will cool the entire atmosphere from 10C to 0C.

someone may have to correct that math.

/boredom

--j_k

Posted by Shigosei (Member # 3831) on :

Where do you think all the heat energy to make those ice cubes went? You're all better off if you shut down your refrigerators. I guess if you already have the ice cubes made, that's one thing, but it would be silly to make more.

Posted by King of Men (Member # 6684) on :

Well, that's not completely obvious. The refrigerators are indoors, in presumably insulated houses. So it would take a bit of time for the heat to leak into the atmosphere. You might be able to take advantage of that time-lag, effectively moving heat from outside to inside for a short period. Heat pumps would do the same thing, and probably more effectively at that.

On the other hand, I don't know how much extra heating you would get in the wires carrying the power to the houses, which is outdoors. American wiring systems are supposed to be pretty inefficient, according to I Read It Somewhere.

Posted by Shigosei (Member # 3831) on :

You're right, I was assuming that all the heat reaches the environment immediately, and not thinking about insulation. But if they just want to cool things down tonight, I guess time does matter.

Posted by aspectre (Member # 2222) on :

Only if ya insulated the houses so well that the heat build-up inside charred the walls burning all the air inside, then started melting the insulation from inside to out.

Of course long before ya reached that particular ignition point, the refrigerators ya started with would cease being within their heat-pump efficiency curve -- ya hafta dump heat into cold; or break the Laws of Thermodynamics, which ain't gonna happen -- and cease functioning as refrigerators to become pure heaters. At least until the wiring insulation melted, and the wires shorted -- producing smoke and possibly flames -- to trip off the house circuit breakers.

Posted by King of Men (Member # 6684) on :

Well, let's rephrase the question a bit. Assume you can move heat from outside the houses to within them with, say, a 10% heat generation (so if you move 100J, you generate 10) which we can assume is vented inside the house, heat-pump style. How many houses would you need, or for a fixed number of houses how much temperature rise would you need, to remove one degree of heat from the atmosphere?

For simplicity we can assume that there is no wind, and ignore conduction, so the air to be considered is basically a column over the county, say one km high. In fact, we can consider a cube one km to a side, for easy numbers. As an approximation, houses are cubes of ten or so meters to the side. Therefore, each house is one one-millionth of the total air volume. So to cool the atmosphere one degree, you have to heat one million houses one degree (which fills up the atmosphere entirely and kind of spoils the point) or half a million houses two degrees; and so on. (In addition there's that ten percent inefficiency factor.) Taking a hundred houses in a square kilometer as a reasonable estimate, we get an increase of 11000 degrees in each of them - in other words, nearly twice the Sun's surface temperature.

Ice cubes, indeed.

This would actually be a rather useful exercise for a physics class. Fun with orders of magnitude, and it also gives a good sense of the sheer size of the world.

Now, we could be clever and start heating up swimming pools instead. That would give us some orders of magnitude leeway in mass and heat capacity.