Chapter 10, Problem 46A

a.

Interpretation Introduction

Interpretation: The value of energy needs to be converted from $462.4\text{ kJ}$ to kilocalories.

Concept Introduction: The conversion factor is a ratio that is widely used to describe the relation between two different units. In order to convert one unit into another, the original unit is multiplied with a proper conversion factor to yield a new unit.

Answer to Problem 46A

  $110.52\text{ kcal}$ .

Explanation of Solution

The conversion factors used are:

  $\begin{array}{l}\text{1 kJ = 1000 J}\hfill \\ \text{1 cal= 4}\text{.184 J}\hfill \\ \text{1 kcal = 1000 cal}\hfill \end{array}$

So, the conversion of $462.4\text{ kJ}$ to kcal is as follows:

  $\text{462}\text{.4 }\cancel{\text{kJ}}\text{×}\frac{\text{1000 }\cancel{\text{J}}}{\text{1 }\cancel{\text{kJ}}}\text{×}\frac{\text{1 }\cancel{\text{cal}}}{\text{4}\text{.184 }\cancel{\text{J}}}\text{×}\frac{\text{1 kcal}}{\text{1000 }\cancel{\text{cal}}}=\frac{\text{462}\text{.4 }\times \text{1000 kcal}}{\text{4}\text{.184}\times 1000}=110.52\text{ kcal}$

Hence, the value of energy $462.4\text{ kJ}$ in kilocalories is $110.52\text{ kcal}$ .

b.

Interpretation Introduction

Interpretation: The value of energy needs to be converted from $18.28\text{ kJ}$ to kilocalories.

Concept Introduction: The conversion factor is a ratio that is widely used to describe the relation between two different units. In order to convert one unit into another, the original unit is multiplied with a proper conversion factor to yield a new unit.

Answer to Problem 46A

  $4.37\text{ kcal}$ .

Explanation of Solution

The conversion factors used are:

  $\begin{array}{l}\text{1 kJ = 1000 J}\hfill \\ \text{1 cal= 4}\text{.184 J}\hfill \\ \text{1 kcal = 1000 cal}\hfill \end{array}$

So, the conversion of $18.28\text{ kJ}$ to kcal is as follows:

  $\text{18}\text{.28 }\cancel{\text{kJ}}\text{×}\frac{\text{1000 }\cancel{\text{J}}}{\text{1 }\cancel{\text{kJ}}}\text{×}\frac{\text{1 }\cancel{\text{cal}}}{\text{4}\text{.184 }\cancel{\text{J}}}\text{×}\frac{\text{1 kcal}}{\text{1000 }\cancel{\text{cal}}}=\frac{\text{18}\text{.28}\times \text{1000 kcal}}{\text{4}\text{.184}\times 1000}=4.37\text{ kcal}$

Hence, the value of energy $18.28\text{ kJ}$ in kilocalories is $4.37\text{ kcal}$ .

c.

Interpretation Introduction

Interpretation: The value of energy needs to be converted from $1.014\text{ kJ}$ to kilocalories.

Concept Introduction: The conversion factor is a ratio that is widely used to describe the relation between two different units. In order to convert one unit into another, the original unit is multiplied with a proper conversion factor to yield a new unit.

Answer to Problem 46A

  $0.242\text{ kcal}$ .

Explanation of Solution

The conversion factors used are:

  $\begin{array}{l}\text{1 kJ = 1000 J}\hfill \\ \text{1 cal= 4}\text{.184 J}\hfill \\ \text{1 kcal = 1000 cal}\hfill \end{array}$

So, the conversion of $1.014\text{ kJ}$ to kcal is as follows:

  $\text{1}\text{.014 }\cancel{\text{kJ}}\text{×}\frac{\text{1000 }\cancel{\text{J}}}{\text{1 }\cancel{\text{kJ}}}\text{×}\frac{\text{1 }\cancel{\text{cal}}}{\text{4}\text{.184 }\cancel{\text{J}}}\text{×}\frac{\text{1 kcal}}{\text{1000}\cancel{\text{ cal}}}=\frac{\text{1}\text{.014}\times \text{1000 kcal}}{\text{4}\text{.184}\times 1000}=0.242\text{ kcal}$

Hence, the value of energy $1.014\text{ kJ}$ in kilocalories is $0.242\text{ kcal}$ .

d.

Interpretation Introduction

Interpretation: The value of energy needs to be converted from $190.5\text{ kJ}$ to kilocalories.

Concept Introduction: The conversion factor is a ratio that is widely used to describe the relation between two different units. In order to convert one unit into another, the original unit is multiplied with a proper conversion factor to yield a new unit.

Answer to Problem 46A

  $45.53\text{ kcal}$ .

Explanation of Solution

The conversion factors used are:

  $\begin{array}{l}\text{1 kJ = 1000 J}\hfill \\ \text{1 cal= 4}\text{.184 J}\hfill \\ \text{1 kcal = 1000 cal}\hfill \end{array}$

So, the conversion of $190.5\text{ kJ}$ to kcal is as follows:

  $\text{190}\text{.5 }\cancel{\text{kJ}}\text{×}\frac{\text{1000 }\cancel{\text{J}}}{\text{1 }\cancel{\text{kJ}}}\text{×}\frac{\text{1 }\cancel{\text{cal}}}{\text{4}\text{.184 }\cancel{\text{J}}}\text{×}\frac{\text{1 kcal}}{\text{1000 }\cancel{\text{cal}}}=\frac{\text{190}\text{.5}\times \text{1000 kcal}}{\text{4}\text{.184}\times 1000}=45.53\text{ kcal}$

Hence, the value of energy $190.5\text{ kJ}$ in kilocalories is $45.53\text{ kcal}$ .