Chapter 6, Problem 1PE

Interpretation Introduction

Interpretation:

The energy present in a chocolate pudding having $\text{140 Cal}$ per serving is to be calculated in joules units.

Concept Introduction:

Energy is defined as the ability to do work, which can be expressed in various units such as $\text{Cal},\text{kcal},\text{J}$ and $\text{kJ}$ etc.

The conversion of units is done by applying the conversion factor, which determines the relationship between two types of units.

Answer to Problem 1PE

Solution: $590\text{kJ}$

Explanation of Solution

Given information: The pudding contains $\text{140 Cal}$ per serving.

Nutritional calories are related to joules as per the following relations:

$\begin{array}{c}\text{1}\text{Cal}=\text{1}\text{kcal}\\ \text{1}\text{Cal}=\text{4}\text{.184}\text{kJ}\\ \text{1}\text{kJ}=\text{1000}\text{J}\end{array}$

Multiply $\text{140 Cal}$ with conversion factors $\left(\frac{\text{1kcal}}{\text{1Cal}}\right)$, $\left(\frac{\text{4}\text{.184kJ}}{\text{1kcal}}\right)$ and $\left(\frac{\text{1000J}}{\text{1kJ}}\right)$ to convert it into joules.

$\begin{array}{c}140\text{Cal}=\left(\text{140 }\bcancel{\text{Cal}}\right)\left(\frac{\text{1}\bcancel{\text{kcal}}}{\text{1}\bcancel{\text{Cal}}}\right)\left(\frac{\text{4}\text{.184}\bcancel{\text{kJ}}}{\text{1}\bcancel{\text{kcal}}}\right)\left(\frac{\text{1000J}}{\text{1}\bcancel{\text{kJ}}}\right)\\ =\text{5}\text{.9}\times {10}^5\text{J}\\ =590\text{kJ}\end{array}$

Conclusion

Hence, the number of joules of energy present in a chocolate pudding having $\text{140 Cal}$ per serving is $590\text{kJ}$.