Help me understand how much heat sink possible with frozen H2O

[maximiliano]

So many questions on this topic...but I guess the starting point would be to explain the reason for the question. That way, maybe someone can help me work backwards to answer the question...and thus I can apply that to other situations.

I have a friend who thinks he can make a personal cooling system, using frozen water (0c) as the coolant. I say that the amount of heat sink capacity of say 128oz of frozen water, is probably way too small to matter, in terms of cooling a person off while climbing a mountain, in 90 F degree heat, for 3 hours. Add to that the weight of the water itself is 8 pounds. It seems to me the ice would be melted and assume the ambient temp so quickly, that little would have happened in terms of cooling the person off...over a 3 hour period of exertion.

So, I'm trying to understand (maybe there's a solid formula for this) how much heat sink is possible, using ice as the sink, and an ambient temp. or 90F...or 99F I guess, since the purpose is to sink energy from the person, which is surely 99F.

I have another question, which is related...but I'll ask it separately.

Thanks in advance as always!

 

[haruspex]

8 lb (3.6kg) ice takes 3.6*334 = 1200 kJ to melt it.
Walking slowly generates 150W. For mountain walking I see a figure of 300W, but I'm not sure whether that is heat generated or power consumed; the difference is that a lot of the energy goes into raising you up the mountain, so does not end up as heat. Let's take 250W.
In practice, some ice will melt as a result of heat from the environment, but suppose we could prevent that; or, at least, suppose that it roughly balances the heat lost by the walker to the environment. 1200kJ/250W = 4800 seconds = 1 hour 20 minutes.
The melted ice would still be cold, so you could get another 20 minutes from that. Better still, use it to wet a bandana, so now you get evaporative cooling too, and the weight reduces.

 

[mrspeedybob]

And the climber has something to drink.

Why start at 0c? Why not start at -40c or -50c? I realize most of the heat is absorbed during melting but starting colder certainly can't hurt.

 

[NascentOxygen]

Why start at 0c? Why not start at -40c or -50c? I realize most of the heat is absorbed during melting but starting colder certainly can't hurt.

No harm in replacing heat stroke by frostbite...

 

[sardar]

First of all, let me start by saying that your questions are very valid and it is great that you are seeking to understand the science behind them. I can offer some insights to help you better understand the concept of heat sink and its potential with frozen water.

Heat sink is the ability of a material to absorb and dissipate heat, thereby reducing the temperature of its surroundings. In the scenario you have described, your friend is looking to use frozen water as a coolant for a personal cooling system. However, as you correctly pointed out, the amount of heat sink capacity of frozen water alone may not be enough to cool a person for a prolonged period of time.

To understand this better, we need to look at the specific heat capacity of water. This is the amount of heat required to raise the temperature of 1 gram of water by 1 degree Celsius. For frozen water (ice), this value is 2.108 J/g°C. This means that for every gram of ice, 2.108 joules of heat energy is required to raise its temperature by 1 degree Celsius.

Now, let's consider the scenario of your friend climbing a mountain in 90°F (32°C) heat for 3 hours. During this time, his body will be constantly producing heat, which will be absorbed by the surrounding air. If he were to use 128oz (3.785 liters) of frozen water as a heat sink, it would have a total heat sink capacity of approximately 802,996 joules (2.108 x 3.785 x 32). This amount of heat energy may seem like a lot, but it is important to note that this is the maximum amount of heat that can be absorbed by the ice before it completely melts.

As your friend continues to exert himself, his body will continue to produce heat, and the ice will continue to melt. Eventually, the ice will reach its melting point (0°C) and any additional heat energy will cause it to melt completely, at which point it will no longer be able to act as a heat sink. This is why you are correct in saying that the ice will likely melt quickly in 90°F heat over a 3-hour period.

In terms of a formula for calculating the heat sink capacity of ice, it is important to consider the specific heat capacity of the material, the amount of material present, and the temperature difference between the material and its surroundings. In this scenario,