Marlene Parrish - What Einstein Told His Cook 2

Another example: Suppose we cut that cubic roast in half parallel to one face. Its surface area will then be increased by 33 percent. The two halves, then, should cook in roughly 33 percent less time than the whole one.

So again, dear, naïve little Virginia, no Santa Claus, or even a reasonably good fairy, exists who can weigh your irregularly shaped rib roasts or turkeys and tell you exactly how many minutes per pound to cook it, even if Wolke’s Law were repealed.

TIME AND TEMPERATURE WAIT FOR NO HAM

I want to roast a piece of meat in an oven for 24 hours at 180°F (82°C). Would this use less gas or electric energy than roasting it for 3 hours at 375°F (191°C)? How about 6 hours at 250°F (121°C)?

This may sound like an odd question, but it was asked of me by the food authority and author Paula Wolfert when she was working on her book The Slow Mediterranean Kitchen: Recipes for the Passionate Cook . Her concept was that long, slow cooking can produce tender, juicy, flavorful meats that higher-temperature cooking cannot match. And as usual, she’s right, as the recipes in her book amply demonstrate (although none of them approaches 24 hours of cooking).

It has always been an oversimplification to say that cooking time and cooking temperature are inversely proportional to each other—that the same, or similar, results can be obtained in a short time at a high temperature as for a longer time at a lower temperature. That concept is woefully inadequate, except over a very limited range of times and temperatures, because cooking is not a matter of simply injecting a given number of calories of heat into a food. As the old jazz song would have it, “It ain’t whatcha do, it’s the way hotcha do it.”

At the time of our discussion, the world was in one of its periodic energy crises, and Paula worried that long, low-temperature roasting might use more energy than shorter, higher-temperature roasting. Fascinated, I leapt at the challenge. Rather than taking the experimental approach, spending days in the kitchen after turning off all electrical devices in the house (it’s amazing how many there are, if you count them) except my electric oven and recording the readings on the electric meter, I decided to take the theoretical approach and try to solve the problem mathematically. Here’s what I came up with.

There are two energy-consuming stages in roasting meat: preheating the oven to the roasting temperature and maintaining that temperature during the roasting period.

It will obviously require more energy to preheat the oven to the higher of the two temperatures. (The actual difference in energy usage will depend on the characteristics of the individual oven.) But in either case the preheating time is short compared with the total roasting time, so we can probably neglect that difference. The difference in preheating times does, however, work in favor of less energy consumption by the low-temperature method.

During the roasting period, the oven will be persistently trying to cool down by losing heat to its surroundings. But whenever its temperature falls to a certain level, the oven’s automatic temperature control feeds in gas or electrical energy to replenish the heat that was lost. Thus, over the entire roasting period, the total energy input should be equal to the total energy lost by cooling. I could then obtain the energy usage under the two roasting conditions by calculating the rates of energy loss by cooling. The average rate of cooling (in calories per hour or Btu’s per hour) times the number of roasting hours should give me the total amount of energy used.

For my calculations I used Isaac Newton’s Law of Cooling (yes, that Isaac Newton), which says that the rate of cooling of a hot body is proportional to the difference in temperature between the body and its surroundings. In this case, the “body” is the air inside the oven, and its surroundings are the air in the kitchen. (The intervening oven walls slow the transfer of heat but don’t change the amount of heat that is ultimately transferred.)

Because all the heat-transfer parameters will differ from one case to the next, I can’t calculate absolute amounts of energy loss. But from Newton’s Law, I can calculate the break-even time : the number of slow-roasting hours at which the energy usage becomes equal to the energy usage in the fast-roasting method. If we slow-roast any longer than this, we will be using more energy than in the fast method.

Here are the results of my calculations. (Gluttons for mathematical detail may consult “(Warning: calculus ahead)” on chapter 9.)

In Paula’s first example, the energy break-even point for slow roasting at 180°F comes out to be about 9 hours. Thus, roasting for 24 hours at 180°F will use substantially more energy than roasting for 3 hours at 375°F. But 24 hours at 180°F is a rather extreme set of slow-roasting conditions anyway.

In Paula’s second example, the energy break-even point for slow roasting at 250°F comes out to be about 5 hours, which is close enough to Paula’s desired 6 hours. So go for it, Paula! The energy police will not break down your door.

What I’ve found, then, is that long, slow roasting need not use more energy than faster, higher-temperature roasting, provided that the slow roasting is not done at too low a temperature. Somewhere between 225 and 250°F (106 and 121°C) is probably the lowest practical limit. But if energy consumption isn’t an issue, by all means pull out the stops and cook your roast at any temperature above about 165°F (74°C) which is hot enough to kill most surface germs. Or do as Paula recommends in The Slow Mediterranean Kitchen : Blast or sear the surface of the meat first to take care of any surface germs before you lower the oven to roasting temperature.

Sidebar Science: (Warning: calculus ahead)

TO COMPAREthe fast ( f ) and slow ( s ) methods of roasting a particular piece of meat to a given state of doneness, we will compare the total amount of oven cooling during fast roasting for h f hours at T f degrees with the total amount of oven cooling during slow roasting for h s hours at T s degrees.

To obtain the number of slow-roasting hours at which the two energy consumptions are equal, we’ll equate the two cooling rates and calculate h s , the energy break-even time for slow roasting.

For this application, Newton’s Law of Cooling can be written

where T is the oven temperature, t is time, and T room is the room temperature. The constant k depends on the specific oven and is assumed to be the same under both roasting conditions.

If the temperature fluctuations in the oven are relatively small compared with the oven temperatures themselves, and if the successive cooling periods are relatively short compared with the numbers of hours of roasting, we can approximate the differential rate of cooling with a temperature difference divided by a cooling time. Moreover, I will assume that the total amounts of time spent in cooling-and-reheating cycles under both sets of conditions are at least comparable. This can be partially justified by considering that the slow, low-temperature roasting, even though lasting longer, will require fewer reheating cycles because of its slower cooling rate.

Using these assumptions, we obtain