When people sleep, their metabolic rate is about 2.6 10-4 C/(s·kg). How many Calories does a 69 kg person metabolize while sleeping 9.0 hours?
? Cal
Multiply that metabolic rate by the mass (69 kg) and the number of seconds in 9 hours. The answer will be in Calories. These are Kilogram Calories, sometimes called "food" calories.
To calculate the number of calories metabolized by a person while sleeping, we can use the formula:
Calories = metabolic rate x time
Given that the person's metabolic rate is 2.6 * 10^(-4) C/(s·kg) and the person's weight is 69 kg, we can multiply these values together:
Metabolic rate = 2.6 * 10^(-4) C/(s·kg)
Weight = 69 kg
Calories = (2.6 * 10^(-4) C/(s·kg)) * 69 kg
Next, we need to convert the time from hours to seconds since the metabolic rate is given in C/(s·kg). To convert hours to seconds, we multiply by 3600 (since there are 3600 seconds in an hour):
Time = 9.0 hours * 3600 seconds/hour
Now we can substitute the values and calculate the number of calories burned:
Calories = (2.6 * 10^(-4) C/(s·kg)) * 69 kg * (9.0 hours * 3600 seconds/hour)
Simplifying the expression:
Calories = (2.6 * 10^(-4)) * (69) * (9.0 * 3600)
Calories ≈ 211.53
Therefore, a 69 kg person would metabolize approximately 211.53 Calories while sleeping for 9.0 hours.