Specific heat
Different substances need different amounts of heat to change temperature, a property called specific heat: the energy needed to warm 1 gram of something by 1 degree Celsius. Dave Arnold uses calories, an outdated scientific unit (the joule is preferred), because they tie directly to temperatures and weights a cook or bartender can picture. Food calories are really kilocalories, 1,000 of these calories.
- Water: a convenient 1 calorie per gram per degree.
- Ice: half that, 0.5 calories per gram per degree. Unless it is melting or freezing, ice can deliver only half the heating or cooling power of the same weight of water.
- Pure alcohol: 0.6 calories per gram per degree.
- Cocktails: water-alcohol mixtures are non-linear, so a cocktail actually needs more energy to warm or cool than either water or alcohol alone. Weird, he says.
Heat of fusion
To melt ice you must add heat. The amount needed is the heat of fusion (enthalpy of fusion), and it works both ways: freezing gives off the same heat that melting takes in. For water it is about 80 calories per gram. That is enough to warm 1 gram of water from 0 to 80 degrees C, or to chill 4 grams of water from room temperature (20 degrees C) all the way to 0.
We take ice for granted, but it is a miraculous substance.
Gram for gram, liquid nitrogen at -196 degrees C has only about 15 percent more chilling power than ice at 0 degrees C. That explains why people new to the technology always underestimate how much liquid nitrogen a project needs.
The freezing point as a balance
The surface of an ice cube in water is never static: molecules are constantly freezing onto it and melting off. If more stick than leave, the ice is freezing; if more leave, it is melting. At 0 degrees C they are in equilibrium. Lower the temperature and the entropy gain from melting becomes small, so water freezes; raise it and the entropy gain beats the heat cost of melting, so ice melts. The freezing point is where the two exactly balance.
What alcohol changes
Take a stirred martini that has just reached 0 degrees C, with ice at 0 degrees and a water-booze mix at 0 degrees. When ice melts into the drink it absorbs the same heat as it would melting into pure water, because it is still pure ice. The entropy change is different: a water-and-alcohol mixture is more disordered than water alone, since there are more ways to arrange water and alcohol molecules than identical water molecules. More available microstates means entropy wins again, and entropy winning means ice melts.
Melting ice absorbs heat and chills the drink below 0 degrees C. With no outside heat source, the heat is drawn from the system itself, so both drink and ice go below 0. As the ice melts and the gin dilutes, the entropy advantage shrinks until a new balance is reached: that balance point is the martini’s new freezing temperature.
The same argument explains why salt added to ice can drop the temperature enough to freeze ice cream. Most children are told only that salt lowers the freezing point of water, which he calls weak; the real reason is the entropy balance above.