Chapter 56, Problem 3.1CT

(a) If Bill, who weighs 160 pounds, consumed 2025 mL of ${\text{O}}_2$ during a six-minute period, what would be his metabolic rate (in units of $kcal/cg/br$ )? (Hint: $\text{1 kg = 2}\text{.2 lbs}$ .)

(b) Assume that, on an average diet, people generate 4.825 kcal of energy for every liter of oxygen they consume. How many calories (kcal) does Bill need per thy? (Hint:

No need to include Bill’s weight in this calculation.)

Summary Introduction

To determine:

The metabolic rate of a person in units of kcal/kg/hr.

Introduction:

Basal metabolic rate is also represented as BMR. It is defined as the rate of the expenditure of energy per unit time at rest by the endothermic animals. The BMR at rest is low as compared to the body undergoing vigorous activities (such as exercise).

Explanation of Solution

Given:

The weight of a person is 160 pounds. 2025 ml of O₂is consumed during a six-minute period.

1 Kg= 2.2lbs. The metabolic rate of the given person can be calculated as follows:

  $\text{a) Weight of person = 160 pounds}$

$\text{In kg- 160 ×0}\text{.45 = 72 kg}$

${\text{O}}_{\text{2}}\text{ consumed}\text{in 6 minutes}\text{=}\text{2025 ml }$

${\text{O}}_{\text{2}}\text{ consumed}\text{in 1 minute = }\frac{\text{2025}}{\text{6}}$

$\text{=337}\text{.5 ml}$

$\text{O2 consumed}\text{in 1 hour = 337}\text{.5 ×60}$

$\text{= 20250 ml}$

$\text{=20}\text{.25 L}$

$\text{1 L of oxygen consumed = 5 kcal}$

$\text{20}\text{.25 L of oxygen consumed = 20}\text{.25×5}$

$\text{= 101}\text{.25 kcal}$

$\text{Metabolic rate = }\frac{\text{101}\text{.25}}{\text{72}}$

$\text{= 1}\text{.41 kcal/kg/hour}$

The metabolic rate of a person is 1.41 kcal/kg/hr.

Conclusion

The metabolic rate of the person in the given condition is 1.41 kcal/kg/hr.

Summary Introduction

To write:

The calories required by the given person per day.

Introduction:

The basal metabolic rate is also represented as BMR. It is defined as the rate of the expenditure of energy per unit time at rest by the endothermic animals. The BMR at rest is low as compared to the body undergoing vigorous activities (such as exercise).

Explanation of Solution

Given:

4.825 kcal of energy is generated for every liter consumption of oxygen on an average diet in people. The calories needed by the given person per day can be calculated as given below:

Oxygen consumption in one hour has already been calculated as 20.25 L.

$\text{Oxygen consumed in 1 hour = 20}\text{.25 L}$

${\text{So in 1 day O}}_{\text{2}}\text{ consumed = 20}\text{.25 × 24 }$

$\text{= 486 L}$

$\text{In}\text{kcal = 486 × 4}\text{.825 }$

$\text{= 2344}\text{.95 kcal}$

The calories needed by the given person per day is 2344.95 Kcal.

Conclusion

The calories needed by the given person per day is 2344.95 Kcal.