## Wednesday, November 28, 2012

### Turkey Diffusion

By Meredith Barthold

Since we just had Thanksgiving and we ate a rather large turkey in my house, I was wondering how much mass the turkey loses as it is baked in the oven. I know the initial weight, and I could have just weighed the turkey after being cooked, but instead I decided to use diffusion to calculate the change in mass after the turkey is cooked. So I measured the turkeys dimensions before putting it in the oven, kept track of the time it took to cook, and I used Fick’s Law of Diffusion.

Most variables were obvious, but the concentration of water inside the turkey is an estimation based on the pressure required to penetrate human skin. It takes 7 bar to penetrate the skin with a needle (http://www.ncbi.nlm.nih.gob/pmc/articles/PMC2291478), and to convert bar to kg/m3, I multiplied 7 bar times the density of air in an estimated 400°F oven, which is 0.5243 (http://www.engineeringtoolbox.com/air-desity-specific-weight-d_600.ntml). This gives an estimation of 3.6701 kg/m3 inside of the turkey.

For the concentration of water vapor outside the turkey I used the same value as was used in class for the water vapor outside the sunflower.

All variables are as follows:
Length of turkey: 35.5 cmà0.355 m
Cross sectional Area of turkey: (0.29 m)*(0.18 m)= 0.0522 m2
Concentration of water vapor outside the turkey: 0.011 kg/m3
Concentration of water inside the turkey: 3.6701 kg/m3
Time in the oven to cook: 5 hrs. 33 mins. à 333 minutes à19980 seconds
Diffusion constant, water vapor in air: 2.4 x 10-5 m2/s

Using the following equation:
Rate of diffusion = Δm/Δt = DA [(C2-C1)/L]
Δm = (2.4 x 10-5 m2/s)(0.0522 m2)[(3.6701-0.011)/(0.355 m)](19980 seconds)
Δm= 0.258 kg = 0.569 lbs = 0.6 lbs

So even though we bought a turkey that weighed 22.6 pounds initially, due to diffusion, the turkey weighed only 22.0 pounds when it was put on our dining room table.