150hw1 - Phys150:Homework1...

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Phys 150: Homework 1 Due in class on Thursday, October 2 nd at 3:30pm in North Hall 1111. From Biological Physics by Nelson 1.3 Metabolism Metabolism is a generic term for all of the chemical reactions that break down and “burn” food, thereby releasing energy. Here are some data for metabolism and gas exchange in humans. food kcal/g liters O 2 /g liters CO 2 /g carbohydrate 4.1 0.81 0.81 fat 9.3 1.96 1.39 protein 4.0 0.94 0.75 alcohol 7.1 1.46 0.97 The table gives the energy released, the oxygen consumed, and the carbon dioxide released upon metabolizing the given food, per gram of food. a. Calculate the energy yield per liter of oxygen consumed for each food type and note that it is roughly constant. Thus, we can determine a person’s metabolic rate simply by measuring her rate of oxygen consumption. In contrast, the CO2/O2 ratios are different for the different food groups; this circumstance allows us to estimate what is actually being used as the energy sourcek, by comparing oxygen intake to carbon dioxide output. b. An average adult at rest uses about 16 liters of O2 per hour. The corresponding heat release is called the “basal metabolic rate” (BMR). Find it, in kcal/hour and in kcal/day. c. What power output does this correspond to in Watts? d. Typically, the CO2 output rate might be 13.4 liters per hour. What, if anything, can you say about the type of food materials being consumed? e. During exercise, the metabolic rate increases. Someone performing hard labor for 10 hours a day might need about3500 kcal of food per day. Suppose the person does mechanical work at a steady rate of 50W over 10 hours. We can define the body’s efficienty as the ratio of mechanical work done to excess energy intake (beyond the BMR calculated in (b)). Find this efficiency.
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1.4 Earth’s temperature The Sun emits energy at a rate of about 3.9 · 10 26 W . At Earth, this sunshine gives an incident energy flux I e of about 1.4 kW m ‐2 . In this problem, you’ll investigate whether any other planets in our solar system could support the sort of water‐based life we find on Earth. Consider a planet orbiting at a distance d from the Sun (and let d e be Earth’s distance). The Sun’s energy flux at distance d is I = I e ( d e / d ) 2 , because energy flux decreases as the inverse square of distance. Call the plant’s radius R , and suppose
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