Question

A sleeping 68 kg man has a metabolic power of 69 W. How many Calories does he burn during an 8.0 hour sleep? Delta E = ________ Cal

Answer 1

Concepts and reason

The concept required to solve the given problem is power.

Calculate the burning energy by using expression for power. Then convert the units of energy from joule to calories.

Fundamentals

The power is defined as the amount of energy transferred in unit time.

The power P is defined as the ration of energy E and time t.

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

The expression for power P is given as follows:

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

Here, E is burning energy and t is time.

Rearrange the above equation for E.

$E = Pt$

The expression for burning energy E is given as follows:

$E = Pt$

Substitute 69 W for P, and 8.0 h for t.

$\begin{array}{c}\\E = \left( {69\;{\rm{W}}} \right)\left( {8.0\,{\rm{h}}} \right)\left( {\frac{{60\,{\rm{min}}}}{{1\,{\rm{h}}}}} \right)\left( {\frac{{60\,{\rm{s}}}}{{1\,{\rm{min}}}}} \right)\\\\ = 1987200\,{\rm{J}}\\\end{array}$

Convert the units of energy from Joule to Calories as follows:

$\begin{array}{c}\\E = 1987200\,{\rm{J}}\left( {\frac{{1\,{\rm{Cal}}}}{{4184\,{\rm{J}}}}} \right)\\\\ = 475\,{\rm{Cal}}\\\end{array}$

Ans:

The calorie of energy burnt by sleep is 480 Cal.