Chapter 15, Problem 15P

To determine

The average metabolic rate of a person.

Answer to Problem 15P

The average metabolic rate of the person is $162\text{J}/\text{s}$ .

Explanation of Solution

Given info:

The time for sleeping is, $t_1=8\text{h}$ .

The time for sitting at a desk is, $t_2=8\text{h}$ .

The time for light activity is, $t_3=4\text{h}$ .

The time for watching TV is, $t_4=2\text{h}$ .

The time for playing tennis is, $t_5=1.5\text{h}$ .

The time for running is, $t_5=0.5\text{h}$ .

Formula Used:

The expression to calculate the average metabolic rate of the person is,

  $M=\frac{t_1{w}_1+t_2{w}_2+t_3{w}_3+t_4{w}_4+t_5{w}_5+t_6{w}_6}{t}$

Here,

  $w_1$ is the energy for sleeping and its value is $70\text{J}/\text{s}$ .

  $w_2$ is the energy for sitting and its value is $115\text{J}/\text{s}$ .

  $w_3$ is the energy for light activity and its value is $230\text{J}/\text{s}$ .

  $w_4$ is the energy for watching TV and its value is $115\text{J}/\text{s}$ .

  $w_5$ is the energy for playing tennis and its value is $460\text{J}/\text{s}$ .

  $w_5$ is the energy for running and its value is $1150\text{J}/\text{s}$ .

T is the total time in one day and its value is 24 h.

Calculation:

Substitute all the values in the above expression.

  $\begin{array}{c}M=\frac{\left[\begin{array}{l}\left(8\text{h}\right)\left(70\text{J}/\text{s}\right)+\left(8\text{h}\right)\left(115\text{J}/\text{s}\right)+\left(4\text{h}\right)\left(230\text{J}/\text{s}\right)+\\ \left(2\text{h}\right)\left(115\text{J}/\text{s}\right)+\left(1.5\text{h}\right)\left(460\text{J}/\text{s}\right)+\left(0.5\text{h}\right)\left(1150\text{J}/\text{s}\right)\end{array}\right]}{24\text{h}}\\ =162\text{J}/\text{s}\end{array}$

Conclusion:

Thus, the average metabolic rate of the person is $162\text{J}/\text{s}$ .