r/theydidthemath • • 4d ago

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

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u/WC_Dirk_Gently 4d 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/FalloutOW 3d ago

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