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.
(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