Question

Rowan's and Jean's rates of energy consumption (which also equal the power expended when doing various activities) are given below:

Rowan:
Activity Rate of energy consumption
Sleeping 75W
Sitting 110W
Studying 120W
Walking 280W
Cycling 400W

Jean:
Activity Rate of energy consumption
Sleeping 55W
Sitting 95W
Studying 105W
Walking 280W
Cycling 400W

(a) What are Rowan's daily energy needs in both kJ and kcal ('food calorie units') if his day consists of sleeping for 8 hrs, walking for 2 hrs, studying for 10 hrs, cycling for 2.5 hrs, and sitting for 1.5 hrs?

Answer 1

Rowan's daily energy needs, based on his activity schedule, are 12,690 kJ and 3,032 kcal. These were calculated by multiplying the power expended for each activity by the time spent, then converting the total energy consumption from joules to kilojoules and kilocalories.

Step-by-step explanation:

To calculate Rowan's daily energy needs, we'll multiply the power expended for each activity by the amount of time spent doing it, converting the watts to kilojoules and kilocalories (kcal).

• Sleeping: 75W for 8 hrs = 75W x 8hr x 3600s = 2,160,000J
• Walking: 280W for 2 hrs = 280W x 2hr x 3600s = 2,016,000J
• Studying: 120W for 10 hrs = 120W x 10hr x 3600s = 4,320,000J
• Cycling: 400W for 2.5 hrs = 400W x 2.5hr x 3600s = 3,600,000J
• Sitting: 110W for 1.5 hrs = 110W x 1.5hr x 3600s = 594,000J

Adding these values together to find the total energy consumption in joules:

2,160,000J + 2,016,000J + 4,320,000J + 3,600,000J + 594,000J = 12,690,000 J (kilojoules)

To convert to kilojoules, we divide by 1,000:
12,690,000 J / 1,000 = 12,690 kJ

To convert joules to kilocalories, we use the conversion factor 1 kcal = 4,184 J:
12,690,000 J / 4,184 = 3,032 kcal

Therefore, Rowan's daily energy needs are 12,690 kJ and 3,032 kcal.