hw1_solutions_F

hw1_solutions_F - CH353M Homework assignment 1(due Friday...

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CH353M Homework assignment 1 ( due Friday Sep. 16 ) 1 (5 points). The beer and ice cream diet ( To simplify calculations and avoid promoting an unhealthy lifestyle beer and ice cream are considered to be water and ice below ) . Nutritionists say that in order to consistently lose weight without much damage to our health, one has to spend an extra 200 kcal per day (note that the US “food calorie” is actually a kilocalorie. Correct units are used on food packages in Europe). a. Suppose you want to achieve this by drinking cold (8°C) water every day. Your body will have to burn extra calories in order to bring the temperature of water up to the normal body temperature, which is about 36.7°C. Calculate how much water one should drink per day in order to comply with this weight reduction plan (you will need to recall the definition of a calorie that I gave in a lecture). The heat capacity of liquid water is 1 cal/g K (from the definition of the calorie). m (g) × 1 (cal/g K) × (36.7 – 8)(K) = 200000 cal m = 6968.6g b. If you did Part a. you probably found out that the required daily amount of water is a bit too large. Consider a diet, in which one eats ice (at 0°C) instead. Use the fact that it takes 6.01 kJ to melt one mole of frozen water (you will learn more about melting later in the course). How much ice should one eat in order to spend 200 kcal this way? The ice should first be melted and then heated from T ice =0 0 C to T body =36.7 0 C 200000 cal = 1000 1 1 6.01( / ) 36.7 200000 1 4.184 18 / J cal x kJ mol K cal kJ J g mol + = , where x is in grams. x = 1716.7 g 2. (10 points) . Thermodynamics of weight lifting . Suppose that, discouraged by the solution of Problem 1, you decided to take up weight training instead and that your idea of weight training is to lift a 200 lbs barbell 100 times during your training session.

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