140 lines
8.1 KiB
TeX
140 lines
8.1 KiB
TeX
% formatted for IOP
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\documentclass[12pt]{iopart}
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\pdfminorversion=4
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\usepackage{float}
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\usepackage{units}
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\usepackage{graphicx}
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\usepackage{hyperref}
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\newcommand{\be}{\begin{equation}}
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\newcommand{\ee}{\end{equation}}
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\newcommand{\bea}{\begin{eqnarray}}
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\newcommand{\eea}{\end{eqnarray}}
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\begin{document}
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\title[How many acres of potatoes does a society need?]{How many acres of potatoes does a society need?}
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\author{N T Moore}
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\footnote{Present address:
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Department of Physics, Winona State University, Winona, MN 55987, USA}
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\ead{nmoore@winona.edu}
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\date{\today}
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\begin{abstract}
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One of the main difficulties in a class on Sources of Energy and Social Policy is the wide variety of units used by different technologists (BTU's, Barrels of oil, Quads, kWh, etc). As every student eats, I think some of this confusion can be resolved by starting and grounding the class with a discussion of food and food production. A general outline for this introduction is provided and two interesting historical cultural examples, Tenichtitlan and the Irish Potato Famine, are provided.
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Science and Social Policy classes are full of bespoke units and involve many different contexts. Starting the class with a discussion of food energy is a nice way for everyone to start with the same context. In addition, discussion of Food Energy can lead to interesting historical claims.
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\end{abstract}
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\noindent{\it Keywords\/}: Energy, Social Policy, kcals, Tenochtitlan, Irish Potato Famine, History, self-reliance
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\submitto{\PED}
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\maketitle
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\section{Introduction}
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When the United States entered World War One one of the problems they faced was logistics. How much food do you need to ship overseas to Europe to feed a million soldiers? That early work in nutrition led to the 3000 Calorie diet many people remember from secondary Health Education class. A bit about units you might remeber: $1~Calorie = 1~kilo-calorie~(kcal)$, and a dietician might build a 3000 kcal diet for a 20 year old basketball player. A \textit{calorie} is the amount of energy it takes to heat a gram of water by a degree Celsius. There are about 4.2 Joules in a single calorie, and a Joule occurs all over introductory physics. If you need to buy a new home furnace, the sales brochure might advertise that it is capable of delivering 100,000 BTU's of heat each hour. What's a BTU? Heat a pound of water by $1^{\circ}F$. Of course Heat Pumps are far more efficient than simply burning methane or propane, but they consume kilo-watt-hours (kWh) of electricity, not BTU's. What's a kWh? Run a 1000 Watt toaster for an hour and you'll have pulled one kWh off the grid, it will cost you about \$0.13 in Minnesota. If you decide to put solar panels in your backyard, they will probably collect about $10\%$ of the 3.5kWh the the sun delivers to each square meter of your lawn (in Minnesota) each day.
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As the previous paragraph illustrates, there are a frustratingly large number of different units in an ``Energy'' class. At Winona State, this 3 credit class fulfulls a ``Science and Social Policy'' general education requirement and is taken by students from across the university. Lots of college majors don't require a math class beyond algebra or introductory statistics and the population is largely math-averse. You could jokingly say that one of the main things students learn in the class is unit converstion, but it isn't far off. Nearly every field finds energy a useful representation, and every profession has their own set of units and terminology that's most well suited for quick calculation. Would a medical lab scientist talk about the fractional acre-foot of urine needed test kidney function? No, but someone in the central valley of California would certianly care about the acre-feet of water necessary to grow almonds! Does a gas station price their gasoline in dollars per kWh? Given the growing electrification of cars, they might soon.
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Everyone eats, maybe not 3000 kcals per day, but at least something every day. When I teach our energy class, I spend a few weeks talking about food energy before all other types. While food production is not central to climate change and wars over oil, food is essential in a way that diesel and gasoline are not. Vehicle fuel makes modern life possible, but we could live, unpleasantly, without it. We can't live without fats and protein.
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\section{Food Energy}
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To introduce Food Energy, I ask the students to work through a few questions:
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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?
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Useful information: the student has a mass of 80kg and is made mostly of water. A Calorie heats 1 kg of water $1^{\circ}C$.
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Answer
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\bea
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3000kcals &=& 80kg\cdot1 \frac{kcal}{kg\cdot C^{\circ}}\cdot\Delta T\\
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\Delta T &\approx& +37.5^{\circ}
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\eea
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Fat tissue serves a valuable purpose, brown fat, babies, songbirds
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What power does the body give off in the more realistic case that the 3000kcal is burned over 24 hours?
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Useful information: $1 kcal \approx 4200J$ and $1 J/s=1W$.
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\be
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\frac{3000kcal}{24hours}\frac{4200J}{1kcal}\frac{1hour}{3600sec}\approx145W
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\ee
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Survival swimming, putting all the kids in one bed on a cold winter night.
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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?
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Useful information: human muscle is about $30\%$ efficient and gravitational energy on Earth's surface has a slope of about $10~Joules/kg\cdot m$.
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Answer
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Energy bar charts
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\bea
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\frac{1}{3}\cdot600kcal\cdot\frac{4200J}{1kcal}
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&=& 80kg\cdot10\frac{Joules}{kg\cdot m}\cdot height\\
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height &\approx& 1000 m
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\eea
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increase in yields since 1917 (graph)
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1917 data
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Grow your own food, possible?
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Grow your own food, how far apart (urban life?)
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\section{Example: How big could Tenochtitlan have been?}
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1917 (A\&M) USDA pamphlet
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Corn for US - area
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If Tenoch was 100k people, how much land area?
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\section{Example: Was the Irish Potato Famine a Natural Disaster?}
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\section{Conclusion}
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%\begin{acknowledgments}
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\ack
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The work was prompted in part by discussions with John Deming, Carl Ferkinhoff, and Sarah Taber.
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%\end{acknowledgments}
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%The command \appendix is used to signify the start of the appendices. Thereafter
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%\section, \subsection, etc, will give headings appropriate for an appendix. To obtain
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%a simple heading of ‘Appendix’ use the code \section*{Appendix}. If it contains
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%numbered equations, figures or tables the command \appendix should precede it and
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%\setcounter{section}{1} must follow it
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\appendix
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\section{Introductory Food Energy Questions}
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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?
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Useful information: the student has a mass of 80kg and is made mostly of water. A Calorie heats 1 kg of water $1^{\circ}C$.
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Answer
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\bea
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3000kcals &=& 80kg\cdot1 \frac{kcal}{kg\cdot C^{\circ}}\cdot\Delta T\\
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\Delta T &\approx& +37.5^{\circ}
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\eea
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Fat tissue serves a valuable purpose, brown fat, babies, songbirds
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What power does the body give off in the more realistic case that the 3000kcal is burned over 24 hours?
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Useful information: $1 kcal \approx 4200J$ and $1 J/s=1W$.
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\be
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\frac{3000kcal}{24hours}\frac{4200J}{1kcal}\frac{1hour}{3600sec}\approx145W
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\ee
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Survival swimming, putting all the kids in one bed on a cold winter night.
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\section*{References}
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\begin{thebibliography}{99}
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\bibitem{nature_cat}
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Marey M
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1894
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Photographs of a Tumbling Cat.
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{\it Nature }
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{\bf 51}
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80
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%https://doi.org/10.1038/051080a0
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\bibitem{Aztec_Cannibalism} for crop productivity
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\bibitem{USDA_1917_yields}
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\end{thebibliography}
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\end{document}
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