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Consider a Spherical Turkey

November 25, 2019

Thursday of this week is Thanksgiving Day in the United States. The traditional meal for this holiday is centered around a turkey. There's a legend that Benjamin Franklin (1706-1790), one of the Founding Fathers of the United States, preferred the turkey to the bald eagle (Haliaeetus leucocephalus) as the US National Bird.[1] This is based on a letter by Franklin to his daughter in which he writes that the turkey, in comparison to the bald eagle, is "a much more respectable Bird, and withal a true original Native of America... He is besides, though a little vain & silly, a Bird of Courage."

A turkey

The common wild turkey is the Meleagris gallopavo.

The precise classification is Animalia, Chordata, Aves, Galliformes, Phasianidae, Meleagridinae, Meleagris.

(A late 19th century woodcut engraved by J. Molten, Library of Congress Catalog No. 2014645207, via Wikimedia Commons)


Physicists often solve difficult problems through simplification, a process that did not meet with the approval of one of my professors when I replaced a Gaussian curve with a triangle to make for an easier calculation. This tendency is summarized in the spherical cow parable that tells of a physicist who was assigned the task of increasing milk production on a dairy farm. He began the presentation his research results with the phrase, "Consider a spherical cow."

A spherical cow would be hard to find, but some prepared turkeys have been likened to balls, and balls are spherical. The Butterball turkey is a pre-brined turkey sold in supermarkets. The brining process, well known to chefs, is a method to trap moisture in meat to promote tenderness. Neither my mother nor my wife brined turkey, but they still tasted great. They also filled the cavity with a bread stuffing, which is safe to do when done with care.[2] One year, my father decided to make an Italian-style stuffing by adding bell peppers. This wasn't a good idea.

Turkey stuffing reminds me of a Bazooka Joe comic I read as a child. These comics were part of the packaging for Bazooka bubble gum. In that strip, Joe doesn't like the taste of a turkey cooked by his friend, Mort, so he asks what Mort used for stuffing. Mort replies that he didn't need to stuff it because it wasn't empty. People raised on supermarket poultry might not get the joke.

Food science is a scientific disciple that combines elements of chemistry, physics, and biochemistry, and its research has given us a better understanding of how to prepare and cook food. While it's possible to do a sous-vide of a whole turkey, this takes nearly an entire day and is recommended only for those with the proper equipment and diligent temperature monitoring. No matter how you cook your turkey, you need to know how long this will take. Reading the information of the plastic wrapper solves that problem; but, what's the physics behind those times?

The United States Department of Agriculture recommends that the minimum internal temperature of a turkey after cooking should be 165°F (74°C). The heat capacity of a turkey determines how long it will take it to reach that temperature when absorbing heat from the high temperature heat reservoir of the oven air. The heat capacities Cp of turkey, some other meats, Salmon, shrimp, and swwordfish, are listed in the table, below.[3]

Food Cp
kj/kg-°C
Cp
Kcal/kg-°C
Beef, hamburger 3.52 0.84
Chicken, broiler 3.22 0.77
Guinea hen 3.14 0.75
Lamb, leg 2.97 0.71
Pork, ham 2.76 0.62
Pork, loin 2.76 0.66
Rabbit 3.18 0.76
Salmon 2.97 0.71
Sausage, beef/pork 2.34 0.56
Shrimp 3.48 0.83
Swordfish 3.35 0.80
Turkey 2.81 0.67
Veal, loin 3.14 0.75
Venison 3.27 0.78

The heat capacities of all these are quite close, with turkey having one of the lowest values by a small percentage. The similarity of turkey's heat capacity to that of pork seems to add credence to the "other white meat" slogan for pork.

Stained glass pig at the Chapelle Notre-Dame-de-Lhor, Moselle, France

Stained glass pig at the Chapelle Notre-Dame-de-Lhor, Moselle, France.

This is a detail from a depiction of Saint Anthony the Great, a.k.a., Saint Antoine l'Ermite (Saint Anthony the Hermit).

(Photo by Pethrus, via Wikimedia Commons


Since I haven't done an experiment in quite a while, I decided to measure the heat capacity of turkey meat. The table value, 2.81 kj/kg-°C, was likely done on uncooked turkey. Since I didn't want to work with that material, I decided to do the experiment with delicatessen sliced turkey, so I purchased a package of Oscar Mayer DeliFresh Oven Roasted Turkey Breast. As a side benefit, I was able to munch on some of the slices while waiting for my data.

For my measurement, I constructed a simple calorimeter from items available to me in my home workshop. A diagram of the calorimeter is shown below. A water bath is used as a heat reservoir whose temperature is monitored by an LM335 semiconductor temperature sensor.[4-6] I wrote about the LM335 is an earlier article (Partial Solar Eclipse at New Jersey, August 24, 2017) in which I described my measurements of the Solar eclipse of August 21, 2017. The calorimeter has a 50 ohm resistor that acts as a heat calibration source. When excited by fifteen volts, the resistor produces 4.5 watts (joules per second) of heat. Stirring is provided for the uniform distribution of heat.

Turkey calorimeter layout

Diagram of the calorimeter for measuring the heat capacity of turkey. (Created using Inkscape. Click for larger image.)


Photographs of the turkey calorimeter

Pretty in pink. The left image shows how fiberglass thermal insulation is used to isolate the calorimeter from the environment. The calorimeter sits atop a piece of Styrofoam on a magnetic stirrer. This Styrofoam platform was necessarily thin to allow functioning of the magnetic stirrer, and this resulted in some temperature drift. The right image shows a detail of the top Styrofoam insulating cap with (left the right) the temperature sensor, the turkey meat specimen enclosed in a thin plastic pouch, and the calibration resistor.


The measurement concept is simple. A turkey meat specimen (17 grams in this case) is first cooled in an external low temperature water bath. When the specimen is then immersed in the calorimeter, it warms by drawing heat from the calorimeter water. The temperature drop of the calorimeter water allows a calculation of the heat capacity. The calibration resistor was energized for two minutes at the start and end of the experimental data collection. Shown below is the conventional method for data extraction from the drifting baseline. The data were taken using an analog-digital converter attached to a computer serial port.

Turkey heat capacity data

experimental data for the turkey meat heat capacity measurement. Since I couldn't assume that the heat capacity of the calorimeter water bath wouldn't change after immersion of the specimen, I did a calibration both at the start and end. There wasn't any change. (Click for larger image.)


Once the heat extracted by the specimen is found, the heat capacity Cp is easily calculated:
Cp = (ΔH/ΔT) = 658j/(22.85-8.00)°C = 44.3 j/°C

44.3 j/°C/17 g = 2.61 j/°C/g = 2.61 kj/kg-°C

This value of 2.61 is strikingly close to the table value of 2.81.

References:

  1. Did Benjamin Franklin Want the National Bird To Be A Turkey?, The Franklin Institute Website.
  2. Turkey Basics: Stuffing, United States Department of Agriculture, Food Safety and Inspection Service Website.
  3. Specific Heat of Food and Foodstuff, The Engineering ToolBox Website.
  4. LM335 datasheet at Texas Instruments (PDF File).
  5. LM335 datasheet at STMicroelectronics (PDF File).
  6. LM335 datasheet at Jameco Electronics (PDF File).

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