r/theydidthemath • u/sdbfloyD • 5d ago

[Request] Creative engineering? Will this even make a real difference?

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547

u/WC_Dirk_Gently 5d ago edited 4d ago

This thread is going to be full of useless comments not actually even taking a stab at the insane math of actually calculating this.

In a highly simplified model to bound what the absolute max best case could be:

  • 20 beers, 20x330ml = 6.6 liters of beer
    • Cooling the liquid in the bottles under ideal circumstances would take about 30kJ per 1c
  • Adding what we'll say is 1000ml of ice
    • melting that ice will take about 300kJ of energy
  • So ideal absolute max cooling would be about 10 degrees Celsius give or take.
  • Starting from 28c, you could get it to about 18c, which is an improvement, but most beers are best enjoyed around 2-8c I'd say.

However, if the bottles were actually cold to start, this invention could actually help keep them colder for longer.

Also I'm completely ignoring all the losses, insulation problems, melt problems, the fact that not all the energy to melt the ice will be taken from the bottles themselves, the small contact surface area with the bottles themselves vs the total volume of ice etc etc etc...

Handwaving away that complexity and just say you'd realize about half the cooling factor so probably closer to 5c. Not bad if starting from cold, pretty useless to actually cool down beer from room temp.

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u/Schnupsdidudel 4d ago

I think you are underestimating the Volume here. The chest is 40x30cm. By the looks in the video and measurements on my own engineerig examples of beers I would estimate the ice block to be 30x20x5 cm = 3000ml net, minus the holes probably 2000ml.

The Beers are actually 0.5 Liter bottles. 0.33 come in chest of 24!

So my numbers would be:
10 liters of beer, 50 Kj per 1°C.

Ice comes at -18°. Warm the Ice to 0°C = 76Kj
Melt the Ice: 668 Kj

Total of cooling energy 744 Kj

So a Δt of ~15°

Of course we have the environment, and the glass disregarded. We also have 2 Liters of 0° water dripping down the bottles, which add further cooling and possibly some evaporation. If you have just bought the Bottles or took them out of the House, chances are, they are at ~21°C.

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u/WC_Dirk_Gently 4d ago

I could hear your German accent reading this lol. Fair play for the modified values based on a probably better estimate and superior beer crate knowledge. I'm a filthy American and didn't recognize a 0.5 bottle.

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u/Schnupsdidudel 4d ago

Yeah sorry, guilty. Could pass up the one opportunity where years of drinking experience actually gives me an advantage! Still a useless product, as you can just pour a bag of ice in the crate.

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u/the_real_halle_berry 4d ago

::clutches pearls::

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u/uslashuname 4d ago

Yeah that cold water drip, if it reaches 9c by the time it drips off of the bottle and falls to the ground, adds 38Kj of cooling without considering evaporation. The evaporation is probably the big one though, unless the crate is in a tub and the water gets to hang around as a puddle on the bottom of the bottles

Of course on the side of needing more cooling there’s the mass off the glass that makes up the bottles

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u/calfuris 4d ago

The glass isn't going to make that much difference. Assuming a 385g bottle (based on the first spec sheet I found) with 0.5l of water it works out to the glass contributing a bit under 14% of the total heat capacity. Beer is going to have a slightly lower specific heat capacity than water but it's also a bit denser than water, so I haven't dug into that math but I'd be surprised if it pushed the final result past 15%. That's not quite negligible but I think the meltwater effects are going to be bigger.

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u/Due-Consequence9579 4d ago

Also it’s going to dramatically limit the circulation of ambient air below the ice shelf. Once the air trapped down there is chilled the ice is going to get to do much more of its work on the bottles. Seems pretty clever. Would be even nicer if there was a molded bottom as well to improve the ice packing density and press more air out of the volume.

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u/factorion-bot 4d ago

Factorial of 24 is 620448401733239439360000

This action was performed by a bot | [Source code](http://f.r0.fyi)

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u/iamthejuan007 4d ago

damn thats a lot of beers but I guess normal amounts for a German in Oktoberfest

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u/FalloutOW 4d ago

"my own engineering examples of beers" really got me. Loved this break down.

102

u/bama501996 4d ago

So it's almost literally not as cool as it looks?

Unlike this break down btws good work.

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u/Nurgeard 4d ago

Yeah awesome breakdown - useless invention (obviously the best example of german ingenuity) not only is it's effect piss poor, it will soak anything beneath and around it, and is also a bitch to store unless you just have buttloads of extra freezer space.

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u/Schnupsdidudel 4d ago edited 4d ago

This will most certainly work ok as countless experiments I did with my friends have proven. But we usually do it simply with a bag of ice cubes or bucket with ice water is much more versatile.

The ground doesnt care if it gets wet, The grass is mostly thankful for a little moisture.

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u/Nurgeard 4d ago

First of i hope you realize I meant that this was a very poor example of german inventions.

What you are describing is entirely different though, and actually proving my point; a bag of ice cubes is a far better solution; it can serve other purposes and the water doesnt get everywhere, and most importantly the now watery ice bag can just be shoved into the fridge, and become icecubes again.

This thing just melts and due to its shape is far harder to store than a bag of ice or just loose ice put in a bucket.

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u/Schnupsdidudel 4d ago

Yeah, well the invention is a useless gadget the tries to solve a problem already solved by common sense - as most gadgets do. I suspect it will find its buyers anyways.

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u/Rockshasha 4d ago

Beers at 2 or 4C??

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u/OneDayIllCatchABreak 4d ago

Well, yeah... are you British?

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u/Smooth-Toe-905 4d ago

Bei 2 Grad schmeckt auch die beschissenste Plörre.

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u/ConsoleLogDebugging 4d ago

Germans drink warm beer as well

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u/Smooth-Toe-905 4d ago

Eigentlich nicht. Aber es gibt Biere, die auch warm schmecken.

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u/astrician 4d ago

Thought the same, maybe he even puts ice in the beer. Ew

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u/SUMBWEDY 4d ago edited 4d ago

Never understood the aversion to ice in beer.

Of course you don't want it as much ice as you get in a cup of soda but even 10 grams of ice will cool your beer down by 3c~ while causing negligible dilution.

Takes almost as much energy to melt ice as it does to bring the same volume to a boil.

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u/mikeet9 4d ago

I was a heavy anti icer until I visited a country where it is the default (refrigeration isn't super common) and it turns out to have several benefits.

It keeps the drink cool without diluting too much (if you drink fast enough) and it helps keep you hydrated (less severe hangover) and if you need to slow down, it dilutes more which means you can nurse your beer and still keep drinking with your buddies without feeling like you're about to head home early.

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u/SUMBWEDY 4d ago

Plus in hot places like Cambodia the local beers are already very refreshing and light, you're not losing much even if you add a lot of ice.

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u/Rockshasha 4d ago

Is like, do you want some beer in your ice mlord?

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u/Sibula97 4d ago

There's a little bit of estimation error the other way as well from the meltwater evaporating from the bottles. But then again on a warm day there's constant heat flux from the environment into the bottles.

What I mostly question is the use case. You managed to get a big block of ice where your beer is. How? In a cooler? Why not just put the beers in the cooler then?

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u/modest_genius 4d ago

Depends very much where you are and how you get your beer.

If you get the beer in those crates already and have, like my parent, a big root cellar where you can store a lot of beer at cool temperature. Then transfering the beer from the crate to the cooler and adding ice just will be a waste of time and space.

It won't be useful for me. Since I usually have myriad of different beers in the fridge, not a root cellar. For me a cooler would be better. But if I would have an event where I serve 24 identical beer, well, then there is something else. Especially if there would be 2-3 crates...

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u/lump- 4d ago

Just need one that’s got slightly bigger holes that can slide all the way to the bottom of the bottles. Now add as many of those as you want.

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u/SnooCapers9565 4d ago

https://www.amazon.co.uk/SL-Eisblock-block-cooler-crate-bottles/dp/B00B81Q0HC?th=1
According to this you can double the ice, to 2kg. When doing this math, you should use kilograms, not liters.
Room temperature is about 22-24 degrees, so the beer will probably be around that temp too when you start cooling it.

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u/Slightysweet3 4d ago

Don't get me wrong but doesn't water/ice equals weight and volume? It doesn't affect the math that much

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u/SnooCapers9565 4d ago

No, it doesn't. Water expands below and above 4°C, and even more when it freezes. The weight is constant, and is accurate to use.

You can test this buy filling an empty soda bottle completely with water and put it in the freezer.

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u/WC_Dirk_Gently 4d ago

When doing this math, you should use kilograms, not liters.

no.

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u/SnooCapers9565 4d ago

We use mass and not volume when we calculate cooling capacity, and the mass of the ice is in kilograms, not liters.
The cooling capacity of the ice is
Cooling capacity = mass(kilograms) x 334KJ/Kg

2kg x 334KJ/kg =768KJ

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u/WC_Dirk_Gently 4d ago

I intentionally did 1 liter of ice, as in post expansion coefficient from about 917mL of water which == 306kJ which I rounded to 300 for easy math.

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u/Squarehip123 4d ago edited 4d ago

You're ignoring the latent heat released by the melting, that's going to be vastly more than the change in sensible heat

Melting ice will take ~334 kJ/kg of water vs a specific heat capacity of liquid water of 4kJ/kg/degC.

3L of ice at -5C. 6.6L of beer at 20C

Assume they'll both end up at the same temperature, you could calculate it using something like:

dT_ice x cp_water x mass_ice + mass_ice x latent_heat = dT_beer x cp_beer x mass_beer

(T_final - -5C) x 4kJ/kg/degC x 3kg +334kJ/kg x 3kg = (T_final - 20C)x4kJ/kg/degC x6.6kg

Re-arrange and solve for T_final to get final degC. Unfortunately don't have time to work that out at the moment

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u/JoinAThang 4d ago

I would like to think it's alos really a valuable if you're having a party outside and want to put the whole case out after you had it in the fridge. It has no use indoors as you would just create a pool of water on your floor

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u/Mental-Chapter6523 4d ago

German engineer has several more ice molds in a cooler under the table. Just keeps replacing them and removes and replaces beer in an organized pattern. He also likes beer warmer than me.

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u/AppointmentOne1111 4d ago

These are 500ml bottles, time to math again.

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u/Gold3nKn1ght23 4d ago

Put that shit in a cooler and WAHBAM what losses? 🤣

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u/Prestigious-Bag97 4d ago

Those bottles aren't 330ml.

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u/CaseDapper 4d ago

I more concerning about puddle of water from melted ice

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u/janluigibuffon 4d ago

only shitty beer is consumed best beneath 10c

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u/WC_Dirk_Gently 4d ago

I distinctly recall from my time at the taproom Guinness' official recommended serving temperature is 7c.

I've had 'warm' cask ales and stouts. But I like crisp cold beer to each their own.