Is filling bathtub with cold water a feasible way to cool apartment?

Question

I live in a 1,000 sq feet apartment without air conditioning here in Toronto, which can sometimes reach 35C during the summer. The cold tap water here is around 7C. If I fill a 100L plastic bathtub with this water and replace the water whenever it warms up to 20C, how long will it take to cool the entire unit?

See if this is correct

E=C*m*dT

so to cool a 92.9 m^2 (1000sqf) by 3 m cube full of air, or 362.31 kg of air, down 10C requires Qa = 1.01 * 362.31 * 10 = 3659.33 Joules of heat.

on the other hand, to warm up 100L (= 100 kg) of water by 10 degrees requires Qw = 4.1813*100*10 =4181.3

so Qw > Qa, thus it seems possible to do this, at least theoretically. Of course my calculations could be wrong. I haven't done this for a while.

I think that everyone will agree that a bathtub full of ice can cool my apartment (if I keep adding ice as it melts), so why can't a bathtub full of ice cold water do the same?

I posed the question to MadSci Network, and here's their reply

http://www.madsci.org/posts/1156463763.Ph.q.html

Answer 1

It will be more a question of the apartment warming up the water, than the water cooling the apartment down.

It's sort of like asking how long it would take for the moon to pull the earth. (yes - they both pull on each other - but the earth will have a bigger impact on the moon than the other way around...)

Answer 2

Adding my voice to all the other answers which seem sound enough to me, I would caution that a tub of water in a warm room will contribute to overalll humidity as it evaporates. Warm air holds more moisture than cold, so by filling the tub with water and allowing it to warm in the room, you are increasing the heat index in the room. 35 will begin to feel much hotter.

A wet towel suspended in front of a fan will provide temporary cooling to those immediately in front of the fan breeze, but it will also contribute to the overall humidity in the room, thus the heat index.

Living in a climate similar to Toronto's, I use fans at nights to exhaust hot air from the house. Put those in the highest windows pointed out. Use other fans, pointed in, at a lower level to bring in cool air from the night. Get up early and close the house.

If you can curtain the exterior of the windows during the day, you can prevent some of the thermal heat build-up.

I live very comfortably without A/C using these methods.

Good luck.

Answer 3

Cool Bathtub

Answer 4

Not really; thermodynamics gets in the way. The water will absorb heat from the air to warm up, thus very slightly reducing the temperature of the air. However, the air is continuing to be heated by the outdoor temperature just as quickly.

Answer 5

just having a tub of cold water in the room wont help anything. Maybe you could have a fan blow across the water, that would create some cooler air in the room...but dont waste the water filling up a tub, it won't do anything by itself.

Answer 6

extremely valuable information and gives me better knowledge

Answer 7

I have never heard of this theory. Chances are it doesn't work.

Answer 8

Only if you sit in it!