Chapter 10, Problem 47A

a.

Interpretation Introduction

Interpretation: The value of energy needs to be converted from $45.62\text{ kcal}$ to kilojoules.

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 47A

  $190.87\text{ kJ}$ .

Explanation of Solution

The conversion factors used are:

  $1\text{ kcal = 4}\text{.184 kJ}$

So, the conversion of $45.62\text{ kcal}$ to kJ is as follows:

  $45.62\cancel{\text{kcal}}\text{×}\frac{4.184\text{ kJ}}{\text{1 }\cancel{\text{kcal}}}=190.87\text{ kJ}$

Hence, the value of energy $45.62\text{ kcal}$ in kilojoules is $190.87\text{ kJ}$ .

b.

Interpretation Introduction

Interpretation: The value of energy needs to be converted from $72.94\text{ kJ}$ 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 47A

  $17.43\text{ kcal}$ .

Explanation of Solution

The conversion factors used are:

  $1\text{ kcal = 4}\text{.184 kJ}$

So, the conversion of $72.94\text{ kJ}$ to kcal is as follows:

  $72.94\cancel{\text{kJ}}\text{×}\frac{\text{1 kcal}}{4.184\cancel{\text{kJ}}}=17.43\text{ kcal}$

Hence, the value of energy $72.94\text{ kJ}$ in kilocalories is $17.43\text{ kcal}$ .

c.

Interpretation Introduction

Interpretation: The value of energy needs to be converted from $2.751\text{ kJ}$ to calories.

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 47A

  $657.49\text{ cal}$ .

Explanation of Solution

The conversion factors used are:

  $1\text{ kJ = 239}\text{.0 cal}$

So, the conversion of $2.751\text{ kJ}$ to cal is as follows:

  $2.751\cancel{\text{kJ}}\text{×}\frac{239.0\text{ cal}}{\text{1 }\cancel{\text{kJ}}}=657.49\text{ cal}$

Hence, the value of energy $2.751\text{ kJ}$ in calories is $657.49\text{ cal}$ .

d.

Interpretation Introduction

Interpretation: The value of energy needs to be converted from $5.721\text{ kcal}$ to joules.

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 47A

  $\text{2}\text{.4}\times {\text{10}}^4\text{ J}$ .

Explanation of Solution

The conversion factors used are:

  $1\text{ kcal = 4184 J}$

So, the conversion of $5.721\text{ kcal}$ to J is as follows:

  $5.721\cancel{\text{kcal}}\text{×}\frac{4184\text{ J}}{\text{1 }\cancel{\text{kcal}}}=23936.664\text{ J = 2}\text{.4}\times {\text{10}}^4\text{ J}$

Hence, the value of energy $5.721\text{ kcal}$ in joules is $\text{2}\text{.4}\times {\text{10}}^4\text{ J}$ .