Want a Perfect Turkey? Calculate Its Specific Heat Capacity

March 20, 2019 | Story | No Comments

As I understand it, the whole point of cooking a turkey is to take it at some temperature and then increase it to a higher temperature. Sure, maybe there's something about family togetherness in there, but really, Thanksgiving is all about thermal transfer. The USDA recommends a minimum internal temperature of 165°F (74°C). I guess this is the minimum temperature to kill all the bad stuff in there—or maybe it is the lowest temperature that it can be and still taste great.

Either way, if you want to increase the temperature of the turkey you need to add energy. Perhaps this energy comes from fire, or an oven or even from hot oil—but it needs energy. But be careful. There is a difference between energy and temperature. Let me give you an example.

Suppose you put some leftover pizza in the oven to heat it up. Since you don't want to make a mess, you just rip off a sheet of aluminum foil and put the pizza on that and then into the oven. The oven is set to 350 degrees Fahrenheit so that after 10 minutes, both the pizza and the foil are probably close to that temperature. Now for the demonstration. You can easily grab the aluminum foil without burning yourself, but you can't do the same to the pizza. Even though these two objects have the same temperature, they have different amounts of thermal energy.

The thermal energy in an object depends on the object's mass, the object's material and the object's temperature. The change in thermal energy for an object then depends on the change in temperature.

In this expression, m is the mass of the object and the variable c is the specific heat capacity. The specific heat capacity is a quantity that tells you how much energy it takes to one gram of the object by 1 degree Celsius. The specific heat capacity of water is 4.18 Joules per gram per degree Celsius. For copper, the specific heat capacity is 0.385 J/g/°C (yes, water has a very high specific heat capacity).

But what about turkey? What is the energy needed to heat up 1 gram of turkey by 1°C? That is the question I want to answer. Oh sure, I could probably just do a quick search online for this answer, but that's no fun. Instead I want to calculate this myself.

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Here is the basic experimental setup. I am going to take a turkey breast (because I am too impatient to use the whole turkey) and put it in a known amount of hot water. I will then record the change in temperature of the water and the change in temperature of the turkey. Of course, this will have to be in an insulated container such that all of the energy that leaves the water will go into the turkey.

With the change in temperature of the water, I can calculate (based on the known specific heat capacity of water) the energy lost. Assuming all this energy goes into the turkey, I will then know the increase in energy of the turkey. With the mass and change in turkey temperature, I will have the specific heat capacity of a turkey.

Just to be clear, I can set the changes in energy to be opposite from each other and then solve for the specific heat capacity of the turkey. Like this.

OK, it's experiment time. I am going to start with 2,000 mL (2 kilograms) of hot water and add it to a foam box with my turkey breast. I will monitor both the temperature of the water and the turkey. Oh, the turkey has a mass of 1.1 kilograms. Here's what this looks like (without the box lid).

I collected data for quite a while and I assumed that the water and the turkey would reach an equilibrium temperature—but I was wrong. Apparently it takes quite a significant amount of time for this turkey to heat up. Still, the data should be good enough for a calculation.

Hopefully it's clear that the red curve is the hot water and the blue is for the turkey. From this plot, the water had a change in temperature of -21.7°C and the turkey had +27°C. Putting these values along with the mass of the water and turkey, I get a turkey specific heat capacity of 6.018 J/g/°C. That's a little bit higher than what I was expecting—but at least it is in the ballpark of the value for water. But overall, I'm pretty happy.

But what can you do with the specific heat capacity for a turkey? What if you want to do a type of sous-vide cooking in which the turkey is placed in a vacuum-sealed bag and then added water at a particular temperature? Normally, the temperature of the water is kept at some constant temperature. But what if you want to start with hot water and cold turkey and then end up with perfect temperature turkey? In order to do this, you could calculate the starting mass and temperature of water that would give you the best ending turkey temperature. I will let you do this as a homework assignment.

Of course there is another way to cook a turkey. You could drop it from some great height such that it heats up when it lands. Oh, wait—I already did this calculation.