Saturday, December 3, 1994

Energy Change and Equivalency?

So this problem has two parts to it and I've been able to figure out part A, but I'm completely stumped on part B.
(a) If you follow a diet of 1850 food calories per day (1850 kilocalories), what is your average power consumption in watts? (A food or "large" calorie is a unit of energy equal to 4.2 103 J; a regular or "small" calorie is equal to 4.2 J.) Note for comparison that the power consumption in a table lamp is typically about 100 watts.

89.9 watts

(b) How many days of a diet of 1850 large calories are equivalent to the gravitational energy change from sea level to the top of Mount Everest, 8848 m above sea level? Assume your weight is 58 kg. (The body is not anywhere near 100% efficient in converting chemical energy into change in altitude. Also note that this is in addition to your basal metabolism.)

Answer on Energy Change and Equivalency?

convert 89.9 W to J/day to get 7.77*10^6 J/day

gravitational energy change is U = mgh where m = 58 kg, g = 9.81 m/s^2, h = 8848 m
U = 58*9.81*8848 = 5.03*10^6 J

P = W/t
7.77*10^6 = 5.03*10^6/t
solve for t and you get that
t = 0.653 days