notes

food_energy.tex

@@ -42,17 +42,29 @@ Planning to save money, one college student decides to go to an all-you-can-eat
 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
+\bea
+3000kcals &=& 80kg\cdot1 \frac{kcal}{kg\cdot C^{\circ}}\cdot\Delta T\\
+\Delta T &\approx& +37.5^{\circ}
+\eea
 Fat tissue serves a valuable purpose, brown fat, babies, songbirds
 
 What power does the body give off in the more realistic case that the 3000kcal is burned over 24 hours? 
-
+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.
 
 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 $10~Joules/kg\cdot m$.
 
 Answer
-
+Energy bar charts
+\bea
+\frac{1}{3}\cdot600kcal\cdot\frac{4200J}{1kcal} 
+	&=& 80kg\cdot10\frac{Joules}{kg\cdot m}\cdot height\\
+height &\approx&  1000 m
+\eea
 
 increase in yields since 1917 (graph)
 
@@ -65,7 +77,7 @@ Grow your own food, how far apart (urban life?)
 
 \section{Example: How big could Tenochtitlan have been?}
 
-1917 (A&M) USDA pamphlet
+1917 (A\&M) USDA pamphlet
 
 Corn for US - area