People of science - a little help, please. There is a fallacy being propagated in pop culture today and I would like to put an end to it. It is being said that spherical ice cubes cool your drink quickly and minimize the dilution. (Humbug, I say!) I would like a proof in the purest form: by math. Not empricaly, like these guys did.
I know the basics here, but I've been out of college far too long to remember the formulas. Yes, I know how to use google but I don't care to. Yes, I've been drinking - shut up.
Assumptions:
Whiskey starts warm, at say 70 deg F.
Ice, either spherical or any other shape with greater surface area, is of identical mass and temperature throughout - say 0 deg F.
Mass of ice is approximately (or exactly, if you prefer) equal to the mass of whiskey.
The drink completely covers the ice in the glass, so you have essentially a cylinder of icy liquid in a glass (both systems have the same boundary conditions.)
The drink is being handled, or swirled Q-family style (back of hand just above the rim in a casual grasp, bottom of glass moved in a circle whilst speaking with a locked gaze on your audience, head tilted slightly downwards.)
OK, do this in the metric system.
First of all, obviously the ice with more surface area will cool faster than a sphere, so don't bother to prove that. The transient response is trivial, so let's move to steady-state. The whiskey-water has cooled to N degrees (frankly, I don't care what that temperature is, but know that it's the same regardless of the ice shape inside the glass, because the thermodynamic boundary conditions are the same, damn it.)
OK, so now that the liquid has cooled to N (32?) degrees, how much ice has melted? I assert that it's the same regardless of the original shape of the ice, but this is where I need your help. In fact, less high surface area ice may have melted than in the sphere given that the center of the sphere may still be <N degrees while the other ice (snowflakes) may be at N.
Second - once cooled to the steady-state temperature, assuming the boundary conditions are the same (air temperature, hand temperature on the glass, etc) can we show that the rate of melting is the same regardless of the shape of the ice? As in, Joules in = grams melted.
This guy kind of gets it, but basically says big cubes are better than small, but I'd like to prove spherical vs non-, with everything else being equal.
Any engineering majors out there taking thermo?