Chapter 2, Problem 15P

Summary Introduction

To calculate: How many watts the human body consumes per second.

Concept introduction:

In cell metabolism process refers to the rotation of ATP production and consumption. ATP is refer as the energy exchange factor that links the anabolism and catabolism process but also fuels processes such as motile contraction, phosphorylation, and active transport. ATP hydrolysis is the process by which the high chemical energy stored in high energy phosphate bonds in ATP is liberated.

Explanation of Solution

Calculation:

Given data,

Human body contains = $5\times {10}^{13}$ cells

Each cell ATP turnover = 10⁹ ATP / 60sec

Hydrolysis of ATP yields = 50kJ / mole = 11.94k cal/ mole $\simeq$12 k cal /mole

1 watt = 1 joule/ sec and there are 4.18 joules/ calories

So,

$\begin{array}{l}\text{The watts consumed by human body = ATP molecules turnover /sec }\times \text{ number of cells/ body }\\ \times \text{mole/Avogadro constant}\times \text{hydrolysis of ATP}\\ \times \text{4}\text{.18 joules/ calories}\end{array}$

$\begin{array}{l}\text{The watts consumed by human body}=\left({10}^9\text{ATP/60sec cell}\right)\times \left(5\times {10}^{13}\text{cells/body}\right)\\ \times \left(\text{mole}/6\times {10}^{23}\right)\times \left(12\text{kcal/mole}\right)\times \left(4.18\times {10}^3\text{J/kcal}\right)\\ =\frac{4.18\times 60\times {10}^{25}}{60\times 6\times {10}^{23}}\text{joule/sec/body}\\ =\frac{4.18\times {10}^{25}}{6\times {10}^{23}}\text{joule/sec/body}\\ =69.66\text{joule/sec/body}\simeq \text{69}\text{.7joule/sec/body}\end{array}$ As, joule/ sec = watt, then 69.7 joule/sec/body = 69.7 watt/body

Hence, human body consumes about 69.7 watt per second.

Conclusion

The human body consumes almost about 69.7 watt per second. Therefore, the human body operates at about the equal wattage like a light bulb.