When people sleep, their metabolic rate is about 2.6 times 10^-4/(s*kg). How many Calories does a 75 -kg person metabolize while getting a good night's sleep of 8.0 hr?
To find the number of Calories metabolized by a 75-kg person during 8 hours of sleep, we need to use the given metabolic rate of 2.6 times 10^-4/(s*kg).
The metabolic rate is given as 2.6 times 10^-4/(s*kg), which means for every second per kilogram, the person will metabolize that amount of energy (in this case, calories).
First, we need to convert the time from hours to seconds because the metabolic rate is given in seconds. There are 60 minutes in an hour and 60 seconds in a minute, so 8 hours can be calculated as:
8 hours * 60 minutes/hour * 60 seconds/minute = 28,800 seconds
Next, we multiply the metabolic rate by the weight of the person to get the total amount of energy expended per second:
Metabolic Rate = 2.6 times 10^-4/(s*kg)
Weight = 75 kg
Energy expended per second = Metabolic Rate * Weight = 2.6 times 10^-4/(s*kg) * 75 kg = 0.0195 Calories/s
Finally, we multiply the energy expended per second by the total number of sleep seconds to find the total energy expenditure during sleep:
Total energy expenditure = Energy expended per second * Total sleep seconds = 0.0195 Calories/s * 28,800 seconds
Calculating this, we find that a 75-kg person would metabolize approximately 561.6 Calories during 8 hours of sleep.