Human muscles have energy efficiency about 25%. That is, out of every calorie of food energy used up by the muscles, only 1/4 calorie is converted to mechanical energy while the remaining 3/4 calorie become heat. During hard exercise, the body looses that heat by sweating: The latent heat of evaporating sweat — 580 cal/g at body temperature — uses up the extra heat produced by the hard-working muscles.
(a) Riding a bike at 20 mph speed on flat ground takes about 175 Watt of mechanical power. If you ride at that speed for one hour, how many calories would you burn?
(b) How much sweat would evaporate off your body to dissipate the extra heat produced by your muscles?
Note that the food calories are actually kilocalories, 1 kcal=1000 cal=4187 J.
(a) Riding a bike at 20 mph speed on flat ground takes about 175 Watt of mechanical power. If you ride at that speed for one hour, how many calories would you burn?
(b) How much sweat would evaporate off your body to dissipate the extra heat produced by your muscles?
Note that the food calories are actually kilocalories, 1 kcal=1000 cal=4187 J.
-
a) 175 W of mechanical power are needed for 1 hour. Since the human body is 25% efficient, it will have to use 4 times that much power in order to produce the mechanical energy required. Total energy used is:
175 W * 4 * 3600 sec = 2,520,000 J * (1000 cal / 4187 J) = 602,000 cal = 602 kcal
So the answer to a is 602 food calories.
b) Of the 602 kcal used by your body, 75% become heat. Then just figure out how much sweat would be evaporated by this energy:
602,000 cal *.75 = 451,500 cal / ( 580 cal / g) = 780 g
So the answer to b is 780 g of sweat.
175 W * 4 * 3600 sec = 2,520,000 J * (1000 cal / 4187 J) = 602,000 cal = 602 kcal
So the answer to a is 602 food calories.
b) Of the 602 kcal used by your body, 75% become heat. Then just figure out how much sweat would be evaporated by this energy:
602,000 cal *.75 = 451,500 cal / ( 580 cal / g) = 780 g
So the answer to b is 780 g of sweat.