A few constants, pulled from the Internet (these are in Joules per gram per degree Kelvin, same magnitude as Celsius):

Specific heat capacity, ice: 2.108 J/g-K

Specific heat capacity, water: 4.20 J/g-K

Specific heat capacity, whiskey: 3.40 J/g-K

Latent heat of melting, ice: 334 J/g

Density of ice: 0.9167 g/cm3

The specific heat of water actually changes a bit with temperature, but not from one glass of water to the next. http://www.engineeringtoolbox.com/water-thermal-properties-d... So If we start with a fluid (whiskey) sitting in a glass (jar?) at room temperature. The whiskey, glass, and air around it are all the same temperature, so there is no net heat energy going into or out of the system. Let’s start with 100 grams of whiskey at 21C. If we then add a lump of ice to it and swirl it around, at some point in time the temperature of that whiskey, the original 100grams of whiskey, will be at an even 15 deg C. At that moment in time, a fixed amount of heat energy must have been removed from the fluid. That amount of energy is calculated with this formula:

Q = cp m dT

Q = (3.4J/g-K) (100g) (21C – 15C)

Q = 2040 J

It doesn’t matter how you cool it, the answer is always the same. You could blow cold air over it, put it in a plastic bag and drop it in the snow, or whatever. In all cases, if you want to get those molecules of whiskey cooled down by 6 degrees, you need to remove exactly 2040 J of energy from them. Any less, and it’s warmer, and more and it’s colder.

In our ice lump case, there is only one way we are comparing removal of that heat energy – by the ice we’ll put it in contact with. Some energy may come from the warming of the ice, some may come from the melting of the ice, and some fraction may come from the melted ice (water) warming up to the same temperature as the whiskey.

If the goal is minimal ice meltage, we would want to design our ice lump to warm up evenly. With 100 grams of ice to work with, and a starting temperature of -10C, it would be possible to cool this measure of whiskey by 6 degrees without even melting any:

Q = (2.108) (100g) (10C) = 2108 J

More than what is needed to cool the whiskey by six degrees, so it’s possible to design an ice lump to cool it without melting. Basically we’d want a lot of surface area and no thick parts to insulate bits of ice – basically every frozen molecule will need to pull their weight in order to cool the whiskey without any of their frozen colleagues melting.

The amount of energy that has to be removed from the whiskey in order to cool to a lower (drinking) temperature of, say, 10C, is:

Q = (3.4J/g-K) (100g) (21C – 10C) = 3740 J

So, now it’s not possible for 100g of ice to cool without melting at least a little. We can calculate the bare minimum of melting (let w = amount of ice melted, in grams):

3740 = (2.108) (100g) (10C) + (w) (344 J/g) + (w) (4.2) (10 - 0)

W = 4.4 grams

This is the minimum amount of ice that has to be melted in order to cool 100g of whiskey from 21C to 10C (using the starting ice lump of 100g at -10C.) If any of the ice in our lump doesn’t warm up to 0C, then some other portion of our lump will have to melt in order to remove that additional energy from the whiskey.

So, design-wise, if any ice is insulated from the whiskey (by being surrounded by more ice) it will not be effective at cooling, and the ice which is at the boundary condition will have to melt.

100g of ice will have a volume of 109.087 cm3. As a sphere, it will have a radius of 29.64mm, giving it a surface area of 110.4 cm2. Compare this to 4 cubes of 250g each – 30.1mm to each side, 217.4 cm2 of surface area – nearly double. This means that the 4 cubes of ice will be able to cool the whiskey nearly twice as fast as the sphere.

Furthermore, the ice at the center of the sphere has nearly twice as much insulation as the ice at the center of the cubes. Because the ice cubes warm more evenly than the sphere, there will be less melting as the fluid passes temperature T (10C).

If we then also consider the time factor, we see the case for the sphere getting even worse. Because it will take longer for the sphere to cool the whiskey, there will be more time for heat to transfer into the whiskey via the warm glass, the warm air, and your warm hand (on the glass). The rate of heat transfer is a function of delta T for each of these boundary conditions. The total heat energy transferred is directly proportional to the time. The longer the spherical ice takes to cool the liquid, the more the liquid will heat up from outside conditions, the more it will have to melt in order to cool to the given temperature.

Spherical ice is the worst possible shape in terms of its ability to cool a drink and not melt into it.