# A blanket and cold stuff

There are some really cool questions out there. Questions that do not require a lot to ask and do not require a lot to answer. Here is one such question (I can’t remember where I first found this question or something like it):

Suppose you put take two identical cans of soda out of the fridge and place them on the floor in the middle of a room. One can you leave alone and one can you cover with a wool blanket. After an hour, you come back and check on the two cans of soda. Which will be warmer?

First, why do I like this question? Mainly because everyone can give an answer. If asked about the ground state energy in an infinite square well, I would get a lot of “dunno”. Second, I like this because it looks at an interesting idea – what does the blanket actually do?

Ask your friends this question, it’s fun. Or, if you are not sure of the answer, try it out.

1. #1 Simon
March 24, 2009

The obvious follow up is to ask why this doesn’t mean we should wear sweaters in the summer to keep cool.

2. #2 Rhett
March 24, 2009

@Simon – perfect!

3. #3 Anonymous Coward
March 24, 2009

Not to be a wet blanket, but to a stickler like me, it seems that this question does require a lot to ask and a lot to answer. Convective heat transport (like most problems in fluid mechanics) is a hard problem.

The answer could work out in any direction depending on stuff like the temperature and thermal mass of the blanket vs. the level of air flow in the room. Diffusion alone is a surprisingly poor method of conducting away heat*, and assuming the can is colder than the room, it won’t be very good at setting up its own convective heat flow.

For example, if the blanket is at room temperature (which is higher than fridge temperature, as was surely implied), has a large thermal mass and has an inner surface in reasonably good thermal contact with the can, it’s not implausible that the heat transport from the blanket’s thermal mass could exceed that of the air in an unstirred room over the course of an hour. Reverse some of those assumptions, and you get the opposite result.

*Diffusion is also a poor method of conducting smells. Working out the diffusion time for a molecule to transverse a normal-sized room gives a result that is surprising to most.

4. #4 Rob
March 24, 2009

I’m not so sure about Simon’s analogy. We’re a heat source of something like 80 to 100 watts.

5. #5 Tom
March 25, 2009

@Rob

I think Simon’s point is that we are a heat source, while the soda can is not (it’s a sink) and that the effect of insulation is to block heat flow — in either direction, which is not the basic understanding some people have. It’s the concept behind the “A thermos is the smartest thing in the world” joke.

6. #6 Dave
March 25, 2009

Wearing a sweater in summer can keep you cooler, at least for a while. Consider the case of where you’re going from one air conditioned building to another, yet you have to cross an open expanse of hot.

Also, consider the case of fire fighters who wear insulated suits while battling fires.

Dave

7. #7 Uncle Al
March 25, 2009

Wool exploits sheep, aluminum rapes the Earth, sugar drives kids psychotic, natives are exploited harvesting cola nuts, carbon dioxide demands the Carbon Tax on Everything, refrigeration looses CFCs, CFHCs, and HFCs destroying the ozone layer. Is there a patriarchal White Protestant European historic oppressor of Peoples of Colour taking the measurements?

Start by crafting an elephant dung paper journal with shared expressions of esteem and personal empowerment. It’s all about diversity. Pass the comment stick!

8. #8 JC
March 25, 2009

In places where people really are hot, they do wear extra clothing in the summer.

The lack of clothing in the summertime in western countries is due to the fact young people figured out a long time ago that advertising works in the reproductive game.

9. #9 Laura
March 26, 2009

The answer to this question is quite simple actually. It all has to deal with the equation for heat loss/heat gain:
Q = K x A (Tcore-Tout)
——————–
D
This problem would affect the distance (D) in this equation. Ultimately the can exposed to the outside air would be warmer. The wool blanket increases the distance between the can and the outside air sort of insulating it.

This also answers the question as to why people wear this clothing in hot weather, because it increases the distance between the skin and the hot air making it harder to gain heat.

*credit to my A&P Professor who taught us this over this week….

10. #10 Laura
March 26, 2009

ok the way the equation showed up, i assume you would all understand this, but the big line is supposed to be under the K x A (Tcore-Tout) so the top is divided by D….just so there’s no confusion.

11. #11 Laura
March 26, 2009

also to add to my first comment, it would prevent the transfer of heat conduction, since the can isn’t physically touching the outside air. It would also prevent heat convection, because the air isn’t touching the can as it blows by.