work

food_energy.tex

@@ -12,6 +12,7 @@
 \newcommand{\ee}{\end{equation}}
 \newcommand{\bea}{\begin{eqnarray}}
 \newcommand{\eea}{\end{eqnarray}}
+\newcommand{\degC}{C^{\circ}}
 \begin{document}
 \title[How many acres of potatoes does a society need?]{How many acres of potatoes does a society need?}
 \author{N T Moore}
@@ -38,23 +39,30 @@ Everyone eats, maybe not 3000 kcals per day, but at least something every day.
 
 To introduce Food Energy, I ask the students to work through a few questions:
 
-Planning to save money, one college student decides to go to an all-you-can-eat buffet each day at 11am.  If he brings homework and stretches the meal out for a few hours he can get all $3000~kcals$ with only one meal bill.  Food is fuel for the human body. If his body burned all this food at once, how much warmer would he get? 
+\subsection{food converted into body heat}
+Planning to save money, one college student decides to go to an all-you-can-eat buffet each day at 11am.  If he brings homework and stretches the meal out for a few hours he can get all $3000~kcals$ with only one meal bill.  Food is fuel for the human body -- could too much fuel make his body feel sick? If his body burned all this food at once, how much warmer would he get? 
 Useful information: the student has a mass of 80kg and is made mostly of water.  A Calorie heats 1 kg of water $1^{\circ}C$. 
 
-Answer
+Possible Answer:
+We'll equate food energy with calorimetric heating and assume human bodies have the same heat capacity as water, about $1kcal/kg\cdot\degC$. This allows us to calculate the body's temperature increase.
 \bea
-3000kcals &=& 80kg\cdot1 \frac{kcal}{kg\cdot C^{\circ}}\cdot\Delta T\\
+3000kcals &=& 80kg\cdot1 \frac{kcal}{kg\cdot \degC}\cdot\Delta T\\
-\Delta T &\approx& +37.5^{\circ}
+\Delta T &\approx& +37.5\degC
 \eea
-Fat tissue serves a valuable purpose, brown fat, babies, songbirds
+Students are normally quite surprised at this answer.  Although it's unrealistic, there is a related phenomena of diet-induced thermogenesis\cite{meat_sweats} known informally as ``the meat sweats''. Some students connect this to feeling quite hungry after a cold swim in the pool (a similar effect).  On a larger scale, talking about what's wrong with this estimate is useful.  The main storage mechanism for storing food energy is fat tissue, which the calculation completely ignores.  Infants are generally born with little fat, and an infant sleeping through the night often coincides with the baby growing enough fat to store enough kcals to make it though a night without waking up ravenously hungry.  A related follow-up is that if a person is stranded in the wilderness, they should immediately start walking downstream (ie, towards civilization) as they likely won't be able to harvest an amount of kcals equivalent to what they already have stored on their hips and abdomen.\cite{trout}  The contrast of bear hibernation \cite{fat_bear} and songbirds constatly eating through the winter are related connections to investigate.
 
-What power does the body give off in the more realistic case that the 3000kcal is burned over 24 hours? 
+Section{Biophysical Power}: 
-Useful information: $1 kcal \approx 4200J$ and $1 J/s=1W$.
+A more realistic question to follow up with relates to the average \textit{power} given off by a person over a day.  
+Again, assuming 3000kcal is burned over 24 hours, with useful information: $1 kcal \approx 4200J$ and $1 J/s=1W$.
 \be
 \frac{3000kcal}{24hours}\frac{4200J}{1kcal}\frac{1hour}{3600sec}\approx145W
 \ee
-Survival swimming, putting all the kids in one bed on a cold winter night.
+Most students still remember $75Watt$ lightbulbs, but given the spread of LED lighting, ``A person is two 75W light bulbs'' will probably only make sense for a few more years.  Desert or cole-weather camping, alone or with friends, and survival swimming are also examples for students to make sense of this answer.  If you can take advantage of other people's waste body heat, you'll sleep more pleasantly.  
 
+Another connection to make is that of ``brown fat'' a sort of biological space heater that humans can develop in response to cold weather.  For example, this tissue's mitochondria can burn lipids and carbohydrates in a useless proton pumping scheme, which produces metabolic heat \cite{Brown_fat}.  Most common in rodents and infants, this mechanism can be stimulated by extended exposure to cold temperatures.  The idea of a biological space heater that takes a month to turn on and a month to turn off matches the lived experience of college students in Minnesota, who wear down jackets in $4\degC$ weather in November, and beachwear in $4\degC$ weather in March.  Additionally, transplants to northern climates often take a few years to ``get used to'' the colder weather up north. It seams just as easy to say that transplants' bodies take a few years to grow the brown fat that allows them to be comfortable with cold weather.
+
+Power is the slope of energy-time
+METS
 Imagine that after eating a $600~kcal$ bacon maple long-john (donut), you decide to go for a hike to work off the Calories.  Winona State  is in a river valley bounded by 200m tall bluffs.  How high up the bluff would you have to hike to burn off the donut?  
 Useful information: human muscle is about $30\%$ efficient and gravitational energy on Earth's surface has a slope of about $10~Joules/kg\cdot m$.
 
@@ -122,14 +130,43 @@ Survival swimming, putting all the kids in one bed on a cold winter night.
 \section*{References}
 \begin{thebibliography}{99}
 
-\bibitem{nature_cat}
+\bibitem{meat_sweats}
-Marey M
+https://www.bonappetit.com/story/meat-sweats
-1894
+P. Trayhurn,
-Photographs of a Tumbling Cat. 
+THERMOGENESIS,
-{\it Nature }
+Editor(s): Benjamin Caballero,
-{\bf 51} 
+Encyclopedia of Food Sciences and Nutrition (Second Edition),
-80
+Academic Press,
-%https://doi.org/10.1038/051080a0
+2003,
+Pages 5762-5767,
+ISBN 9780122270550,
+https://doi.org/10.1016/B0-12-227055-X/01188-3.
+(https://www.sciencedirect.com/science/article/pii/B012227055X011883)
+
+\cite{trout}
+The wilderness river might be full of trout, but if they're 300kcals each, you'll have to catch, clean, and smoke $10$ of them to store up a day's food. \url{https://fdc.nal.usda.gov/fdc-app.html#/food-details/175154/nutrients}
+
+\cite{fat_bear}
+Some sources claim that bear metabolism can vary between 4000 to and 20,000 kcals per day, \url{https://bear.org/5-stages-of-activity-and-hibernation/}, comically illustrated by the National Park Service at \url{https://www.nps.gov/katm/learn/fat-bear-week-2022.htm} .
+  
+\bibitem{brown_fat}
+A space heater
+\url{https://hms.harvard.edu/news/research-brown-fat-heats}
+
+Brown and Beige Fat: Molecular Parts of a Thermogenic Machine
+Paul Cohen1 and Bruce M. Spiegelman2
+Diabetes 2015;64:2346–2351 | DOI: 10.2337/db15-0318
+
+https://pubmed.ncbi.nlm.nih.gov/33846638/
+Shamsi F, Piper M, Ho LL, Huang TL, Gupta A, Streets A, Lynes MD, Tseng YH. Vascular smooth muscle-derived Trpv1+ progenitors are a source of cold-induced thermogenic adipocytes. Nat Metab. 2021 Apr;3(4):485-495. doi: 10.1038/s42255-021-00373-z. Epub 2021 Apr 12. PMID: 33846638; PMCID: PMC8076094.
+
+https://pubmed.ncbi.nlm.nih.gov/14715917/
+Cannon B, Nedergaard J. Brown adipose tissue: function and physiological significance. Physiol Rev. 2004 Jan;84(1):277-359. doi: 10.1152/physrev.00015.2003. PMID: 14715917.
+
+https://pubmed.ncbi.nlm.nih.gov/6722594/
+Himms-Hagen J. Nonshivering thermogenesis. Brain Res Bull. 1984 Feb;12(2):151-60. doi: 10.1016/0361-9230(84)90183-7. PMID: 6722594.
+
+https://www.nih.gov/news-events/nih-research-matters/uncovering-origins-brown-fat
 
 \bibitem{Aztec_Cannibalism} for crop productivity