Lets say you have an enclosed space 3 meters x 2 meters x 1 meter. The space is a uniform 40 C. Now, you magically manifest 10 kg bags of ice inside of this box. Show For the simple problem: How many bags of ice will it take to cool down the box to 20 C in 24 hours? For the advanced problem: How many bags of ice will it take to cool down the box to 20 C in the fastest time possible? (I don't know if this is possible to do due to too many unknowns) Constraints:
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Cooling a room
Our air conditioner has broken so i was bored and started thinken about something. I calculated that a 10 pound bag of ice will cool my room (which i figured is about 4500 ft^3... yah... i love my room lol) from about 86 freaken degrees!! to about 72 degrees fahrenheit. In my calculations i used the specific heat of dry air by the way :-/... but this is more of a excercise then
hoping for a real world solution. Anyhow, does that 14 degree drop seem reasonable?? Not looking for an exact figure or anything because i know theres too many things going on for that that i couldnt account for... just wondering if it sounds reasonable. Answers and Replies
That delta T seems very high to me, especially without any forced convection. A 10 pound bag of ice is only a couple of bucks. Why not do an experiment?
Looks resonable! [tex]L_{ice} >> c_{air}[/tex]
That delta T seems very high to me, especially without any forced convection. A 10 pound bag of ice is only a couple of bucks. Why not do an experiment?
Yah theres a lot that wasnt taken into account... it was just a thought experiment to say the least. I might put a big block right next to me though and see if it'll just cool me down lol
It wouldn't work in practice because the ice needs time to melt and meanwhile hot air and radiation come continuously from outside. However, the calculation itself looks sound: it just takes into account the static situation the ice absorbs heat from the air - in a
perfectly insulated room. Just to make sure, you did add both the heat absorbed by melting the ice and the heat absorbed by heating the water from 32F to 72F, right? Little random, useless tidbit - the cooling capacity of air conditioners is measured in "tons" which is actually referring to tons of ice, used in springhouses. Someone (maybe Fred) said recently that that's the rate of cooling provided by melting a ton of ice in a day, but I thought it was a longer
timeframe. I guess I could calculate it if I wasn't so damn lazy...
Yah i added in the melting water along with it heating up to ambient.... air conditioners worken now i think so im happy though :D
One ton = 288,000 btu/day which is approximately the heat of fusion of 1 ton of ice at 32°F
Fred is right about the definition of Ton(actually TR-Ton Refrigeration). You can extract about 184 btu per pound of ice(144btu/pound latent and 40btu/pound sensible heat). So this will aproximately reduce the room temperature by 22.71F(184*10 = 0.075*4500*0.24*dT) But the average heat load for a residential building will be 1ton/450 sq.ft so considering a 10ft. height room,
you have to remove heat at the rate of 12000btu/hr.
The calculation sounds about right. The problem with actually doing this in a room is the large amount of thermal mass in the room. All the furniture, walls, everything in the room will also reject heat to the air. Because of the huge surface area, that heat rejection is relatively efficient - the heat from the room/objects in the room can overcome the cooling of the ice very
easily. Note: The thermal mass of the room/objects is a transient which is different from the steady state heat transfer. You won't get much heat transfer from the environment untill you cool down the thermal mass of the room/objects. Suggested for: Cooling a room
Can you cool a room with a block of ice?According to the GHI, placing a bucket of ice in front of a fan as a homemade AC unit is just as effective. 'As the air passes over the ice it will be chilled and will circulate refreshingly cold air around the room,' they explain.
Does blowing a fan over ice cool a room?Does using ice and a fan help with warm air? Fans circulate air to keep a space cool. As the ice cubes melt due to the warm temperatures, the fan will blow that cool result from the ice cubes, causing a cooling effect in the room. During a hot day, even one fan and a bowl of ice cooling a room will help.
How many Btus are in a block of ice?The reason that you use ice in your beverage cooler instead of cold water is the cooling capacity of melting ice. If you put your beverages down in 32° water, it only takes one-half of a Btu to raise the temperature to 33°. With ice it takes 144 Btus to melt one pound of ice at 32°.”
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