Posted by Dave Arnold

Last week I participated in a seminar at Tales of the Cocktail entitled, “The Science of Shaking.” The panel was put together by moderator Eben Klemm (head of bar programs for the B. R. Guest restaurant empire, well-known innovative cocktail guy, and former biologist) with Alex Day (famed bartender from Death & Company and Franklin Bar) and myself as panelists.

Before I post the results of the seminar, I wanted to do a short post on some basic cocktail science. I am not a scientist, so please feel free to correct me.

Question: If ice melts at 0° Celsius, and I start with 0° ice, how is it possible that shaken drinks can get down to minus 7° Celsius?

Answer: First of all, yes, shaken drinks can get down to minus 7° just by shaking with ice.

Well, we all know that alcohol freezes at a much lower temperature than water, but that still doesn’t answer the question: how can ice make something colder than 0°?

This question can be approached several ways (colligative properties, vapor pressure, etc.), but I think the most fundamental way is to see the problem as a balance of changes in enthalpy and entropy. In other words, molecules are lazy but they also like to be free.

In any reaction, a change in enthalpy is a measure of the heat absorbed or released during that reaction (assuming a constant pressure, yadda yadda). In general, all things being equal, things want to give off heat. By giving off heat they have a lower internal energy. Things want to go to a lower energy state. Things are lazy. It takes energy to break ice molecules free of the crystal lattice, so there is less energy stored in an ice cube than in water at the same temperature and pressure (cause I had to dump in heat to make it into liquid water). This heat that has to be added to ice to make water is called the enthalpy of fusion (or the heat of fusion). The heat of fusion of water is about 80 calories per gram, meaning that the heat required to melt one gram of ice is sufficient to heat one gram of water all the way from 0° to 80° C! Remember: melting ice requires heat (the heat comes from your drink so your drink gets colder). Making ice gives off heat, so enthalpy favors water turning to ice.

Entropyis a different story. Entropy is often described as a measure of disorder. Greater entropy equals greater disorder. A better way to think about it is as a measure of how many different states something can be in (scientists call these microstates). Things want to increase in entropy. Things want to maximize the number of available microstates and then commence to occupy those microstates in a random way. Things want to be free. At any given temperature, there are more positions, speeds, etc.—microstates—in a liquid than in a solid. Water molecules, for instance, are free to spin around and find new neighbors, etc. Ice molecules are locked in a crystal. Being a solid is more constrained than being a liquid, so entropy favors ice melting into water.

So who wins, enthalpy or entropy? It depends on temperature. As the temperature goes up, entropy tends to dominate and ice melts. As the temperature goes down, the heat of fusion tends to dominate and water freezes. At high temperatures, entropy wins because there are more microstates available to the molecules in the liquid water than at lower temperatures (cause they are moving around more). Thus, there is more of an entropy win by turning to a liquid than at lower temperatures. The freezing point of water (0° C) is the point at which the entropy gain from ice melting to water is exactly balanced by the amount of heat given off by water freezing into ice. Water molecules are constantly freezing into ice and melting into water at the same rate—they are in equilibrium. If you lower the temperature, the entropy gain becomes puny and water wants to freeze. If you raise the temperature, the entropy win outstrips the enthalpy part and the ice wants to melt. Got it?

What happens when you add alcohol? For the purposes of this discussion, let’s assume that the ice crystals remain pure water (that’s pretty true). Ok. We are at 0° C, we have ice and water at equilibrium, and we add alcohol into the liquid water. The heat given off by water molecules freezing into ice is the same as it was before, because the ice hasn’t changed; but the entropy win of ice melting into the water/alcohol mix has gone up. Ice melting into the water/alcohol mix has more microstates available, more ways of being arranged than were available in the pure water, because there are more different ways of arranging x water molecules and y alcohol molecules than there are of arranging x+y water molecules. So what happens? The entropy gain of melting wins and the ice starts to melt. Melting ice absorbs heat. The only place the heat can come from is from the ice and water/alcohol mixture (oh yeah, I forgot to mention I am assuming a closed system), so the whole shebang cools down below 0°.

What’s really cool is that as the ice melts, the solution gets more diluted, which reduces the magnitude of the entropy win at the same time as the temperature goes down. This happens until a new equilibrium is reached, when the entropy and enthalpy become balanced again—that is the new freezing point of your drink. The theory is pretty straightforward but figuring out the final temperature and dilution of a drink from first principles is well, well beyond my ability. I encourage you to try and tell us how. One note before you try, though: I’d say it’s probably a lot harder than you think. Even assuming a closed system (false), and no energy input from shaking (false), and no problems with surface area and speed of agitation and quantity of ice vs mixture (somewhat false), it’s a hard problem to solve exactly.

Next installation: Tales of the Cocktail Seminar: The Science of Shaking, does type of ice matter?