Question

If someone's diet includes 2,000 calories/day, calculate the average power this represents in watts over a 24-hour period. 1 food calorie equals 4,187 KJ.

Answer 1

96.92 watts

Step-by-step explanation

Step 1

find the energy of a day( 24 hours)

to solve this we can use a rule of three, then let x represents the energy in 2000 calories

if

`\begin{gathered} 1\text{ food calorie}\Rightarrow4.187k\text{ J} \\ \text{then} \\ 2000\text{ calories}\Rightarrow x \end{gathered}`

so, the proportion is

`(1)/(4.187)=(2000)/(x)`

solve for x

`\begin{gathered} (1)/(4.187kj)=(2000)/(x) \\ \text{cross multiply} \\ 1\cdot x=2000\cdot4.187 \\ x=8374k\text{ j} \\ x=8374000 \end{gathered}`

hence, So a 2000 calorie diet corresponds to about 8.37 million joules

Step 2

now, we need to find the power (power is the amount of energy transferred or converted per unit time)

`Power(watts)=\frac{\text{work done(Joules)}}{\text{time(seconds)}}`

then ,let

work done= energy= 8374000 Joules

-we need convert hours into seconds, to do this, just multiply the number of hours by 3600 to obtain the time in seconds, so

`24\text{ h}\Rightarrow24\cdot3600\text{ sec}\Rightarrow86400\text{ seconds}`

now, replace in the formula

`\begin{gathered} Power(watts)=\frac{\text{work done(Joules)}}{\text{time(seconds)}} \\ Power(watts)=\frac{8374000\text{ Joules}}{86400\text{ seconds}} \\ Power(watts)=96.92\text{ watts} \end{gathered}`

therefore, the answer is 96.92 watts

I hope this helps you