Question

A sleeping 68 kg man has a metabolic power of 71 W . How many calories does he burn in 8 hours of sleep?

Answer 1

Answer:

$4.87\cdot 10^5 cal$

Explanation:

Power is related to energy by the formula:

$P=\frac{E}{t}$

where

P is the power

E is the energy used

t is the time taken

In this problem, we know the power, P = 71 W, and the time taken:

$t=8 h \cdot 3600 =28800 s$

so, the energy burned is

$E=Pt=(71 W)(28800 s)=2.04\cdot 10^6 J$

And since 1 cal = 4.186 J, we can convert into calories

$E=\frac{2.04\cdot 10^6 J}{4.186}=4.87\cdot 10^5 cal$

Answer 2

Answer:

Energy, E = 488.71 calorie

Explanation:

It is given that,

Mass of the man, m = 68 kg

Metabolic power of the man, P = 71 W

Time taken, t = 8 hours = 28800 s

Let E is the amount of energy transferred in given time. It can be calculated as :

$E=P\times t$    

$E=71\ W\times 28800\ s$

E = 2044800 J

or

E = 2044.8 kJ

Since,

1 calorie = 4.19 kJ

E = 488.71 calorie

So, he burn 488.71 calorie in 8 hours of sleep. Hence, this is the required solution.