Water/Saltwater energy storage

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davel

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Bunch of rocket scientists here, this should have a simple answer.

I have a small portable freezer for the car. It can drop the internal temperature to -4°F. I do not want to have it drawing it's required 5 amps when the car is not running for obvious reasons.

I have gallon jug that I can fill with water and put in the freezer. The freezer will freeze this water at about 32°F and take if further down to about 0°F. How much energy will this one gallon of water absorb before becoming liquid again at 32°F?

Now, instead of pure water, I use a 18% NaCl solution in the gallon jug. If will freeze into slush at about 5°F and continue to cool to about 0°F. How much energy will this one gallon of saltwater absorb before becoming liquid again and reaching 32°F?

IOW, am I better off using pure water or saltwater as a cold storage medium?
 

Zeus-cat

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What you are asking is what about is referred to as the latent heat of fusion. How much energy is required to convert X amount of water to ice.

This is a straightforward calculation in metric. One calorie raises or reduces one gram of water one degree C. To turn water at 32F to ice at 32F you need to extract 80 calories per gram. I'll let you do the math. Not touching the salt version of this.

Note: one calorie is the metric calorie and not the food calorie people use in the US. One US calorie is actually a kilocalorie everywhere else in the world.

See this for more info:
Latent Heat and Freezing and Boiling Points | EARTH 111: Water: Science and Society (psu.edu)
 

dhbarr

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Use coldpacks instead of saltwater?
 

Kelly

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Seat of the pants answer, as a former Chem Engineer: Adding salt to water will significantly change the melting point, but not so much the heat capacity or heat of fusion. In fact, adding salt will decrease these, so if you want to get the most heat (cold) storage, you're better off with pure water.

And, as the numbers from Zeus indicate, you get far more heat from the phase change (freezing) than you do from the temperature change, so you definitely want to use something that will freeze solid at the given temperature, not merely turn to slush - so again, plain water is better.
 

davel

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Well, in both cases the water or saltwater is taked below the freezing point, so heat of fusion is involved in both cases. Specific heat of ice is significantly less that the specific heat of water, so my thought was that adding the salt to keep it liquid might increase the total heat capacity. Comes down to how much of a difference there is between the heat of fusion of pure water vs salt water, and if the specific heat of salt water is significantly less that that of pure water.
 

BMcD

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I think saltwater has the same heat of fusion as water. Saltwater does have a lower specific heat. If the premise that saltwater has the same heat of fusion is correct, then I think you will be better off with fresh water, but you are correct that there is a wrinkle. Sea water (let's assume that's what you mix up) has a melting point of -2C, so you are getting two more degrees celsius of the higher specific heat associated with liquid saltwater vs. freshwater ice.
 

Reinhard

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The short answer: If you need to keep the contents at least somewhat cool for as long as possible, use pure water. If you need to keep the contents below freezing, add salt, but not so much that it stops freezing.

Longer answer:
There are two different aspects that counteract each other a bit. As has already been pointed out by others, much more energy is required to melt water than to heat it up a couple degrees (Heat capacity of water: 4.2 kJ/kg*K, heat capacity of water ice: 2.1 kJ/kg*K, heat of fusion: 334 kJ/kg).
The energy required to bring an amount of water from -4°F to room temperature adds up as follows: About 9% to heat the ice to its melting point, 69% to melt it and 22% the heat the liquid up to room temperature. If you put a thermometer into your water jug, you'd observe a relative quick rise to 0°C/32°F, than the temperature dwells for a while at 0°C/32°C followed by a slower rise to room temperature. @Zeus-cat already posted a link that shows this nicely.

What happens if you add some - but not too much - NaCl to the water? First of all, the heat capacity gets reduced a bit, so the jug is able to absorb less energy before reaching room temperature. But it also decreases the melting point. Instead of dwelling at 0°C/32°F most of the time, it will dwell at a lower temperature.
While it is powered off, the water jug will be the coldest part of your freezer, everything else will be at least a bit warmer. Whatever temperature you need to keep, the melting point of your water/NaCl solution needs to be lower. So if it is important for you to keep the content of your freezer below 0°C/32°F, you need to depress the freezing point of your cold storage accordingly. The exact numbers vary based on a couple factors and it is probably easier to just try it out.

Disclaimer: The actual freezing/thawing of water/NaCl solutions is a bit more complicated, and I'm likely missing a couple of details.

Reinhard
 

davel

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Thank you for that thorough answer.
The actual freezing/thawing of water/NaCl solutions is a bit more complicated, and I'm likely missing a couple of details
Yeah, I wasn't having any luck finding actual numbers for salt water, that why I though I'd ask.
 

Reinhard

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Yeah, I wasn't having any luck finding actual numbers for salt water, that why I though I'd ask.
As I understand it, there is no sharp transition between liquid and frozen with salt water, but a separation where part of the water freezes while the salt becomes concentrated in the remaining liquid. Therefore, there is no single heat of fusion number, but a number that can be associated with a given temperature range. The best I found was this paper:
See for example table 3 and fig 2. For the highest listed salinity 1.2% (note the per mille sign, I initially misread that as a percent sign), one can see that more than half of the heat capacity resides within a single degree Celsius (-0.7 to -1.7). Unfortunately, the listed salinity and temperature numbers are quite a bit off from your plans, so it's hard to estimate how much capacity you lose. There are formulas though, that should give you at least a ball park number.

Reinhard
 

davel

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Thanks, after looking at that paper, I think I will go trial and error :).
 

Marc_G

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Rather than quibble about a few calories, maybe a practical concern is more relevant? Is there a greater risk to either water or salt water? Will the gallon jug of water expand on freezing more than the saltwater situation, potentially leaking or bursting? It is the risk of leaking salt water as a more corrosive agent a risk?
 

davel

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A 2200 mile road trip is coming up. The gallon jug I use is rectangular in shape. I can somewhat compress the sides when I fill it, so some expansion can be accommodated. My puppy dog likes Stella and Chewys chicken nuggets for lunch - these must be kept frozen, or they turn to mush and she won't eat them. Yes, she is very spoiled.

My current 15% NaCl is not freezing very solid, so I'm going to try 10%.
 

dhbarr

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Cold packs can be had that freeze at 18f....
 

BMcD

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At the risk of poisoning your food, maybe a pack with a very mild antifreeze solution?
 

Sooner Boomer

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Antifreeze does'nt mean it *won't* freeze, it just means it will freeze at a MUCH lower temp. Unfortunately, it will also reduce the density and specific heat (both abilities to cool other stuff).
 

BMcD

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Antifreeze would prevent the solid-liquid phase change that actually stores / absorbs much of the heat, maintaining temperature.
The idea behind “very mild” solution was to try to get the freezing point down without getting it so far down it won’t freeze. If the idea is to keep things colder than 32F for as long as possible then shooting for the lowest freezing point possible seems a reasonable strategy. But as pointed out above, you give up a lot of specific heat in the solid and liquid phases, and I have no idea what some AF will do to the heat of fusion. Just trying to turn the OP’s road trip into a science fair project.
 

davel

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OK, seemed to be some interest, so here are my results.

This is an AstroAI Protable Freezer, https://www.astroai.com/product/Astroai-Portable-Freezer-15l
Cavity: 15L, about 0.5 cu ft.
Load: Rectangular gallon jug filled with 10% NaCl and water (w/w)

Allow to run a couple of days to be sure the 'load' is fully frozen.

Reset thermostat to +32 (leave unit powered so I can use its built in thermometer)

Start - temp 0°F
1 hr - +13°F
3 hr - +14°F
6 hr - +18°F
9 hr - +20°F
16 hr - +29°F

Adding additional load should just make it better. Looks like it will keep the dogs food well below freezing for at least 12 hours, unpowered. It does take up to 18 hours to fully refreeze the 'ballast'.
 
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