Chapter 10, Problem 25A

(a)

Interpretation Introduction

Interpretation: Conversion of 75.2 kcal to joules and kilojoules needs to be performed.

Concept Introduction: In metric system, Calorie is the amount of energy (heat) required to increase 1 g of water by $1\text{°C}$ . The conversion factor used to convert calories into joules is $\frac{\text{4}\text{.184J}}{\text{1}\text{cal}}$ and conversion of kcal into kilojoules is $\frac{\text{4}\text{.184}\text{kJ}}{\text{1}\text{kcal}}$ .

Answer to Problem 25A

The value of 75.2 kcal in joule is $\text{3}\text{.15}\times {\text{10}}^5\text{J}$ and in kilojoules is $314.64\text{kJ}$ .

Explanation of Solution

Convert 75.2 kcal into joules:

  $\begin{array}{c}\text{1}\text{kcal=1000}\text{cal}\\ \text{75}\text{.2}\text{kal=75}\text{.2×1000}\text{cal}\\ \text{=75200}\text{cal}\end{array}$

Since,

  $\begin{array}{c}\text{1cal=4}\text{.184}\text{J}\\ \text{75200}\text{cal=}\frac{\text{75200}\text{cal}\times \text{4}\text{.184}\text{J}}{\text{1cal}}\\ \text{=314636}\text{.8}\text{J}\\ \text{=3}\text{.15}\times {\text{10}}^5\text{J}\end{array}$

Conversion factor for kilocalories to kilojoules is $\frac{\text{4}\text{.184}\text{kJ}}{\text{1}\text{kcal}}$ .

Therefore, convert 75.2 kcal into kilojoules as follows:

  $75.2\text{kcal}\times \frac{\text{4}\text{.184}\text{kJ}}{\text{1}\text{kcal}}=314.64\text{kJ}$

(b)

Interpretation Introduction

Interpretation: Conversion of 75.2 cal to joules and kilojoules needs to be explained.

Concept Introduction: In metric system, Calorie is the amount of energy (heat) required to increase 1 g of water by $1\text{°C}$ . The conversion factor used to convert calories into joules is $\frac{\text{4}\text{.184J}}{\text{1}\text{cal}}$ and conversion of kcal into kilojoules is $\frac{\text{4}\text{.184}\text{kJ}}{\text{1}\text{kcal}}$ .

Answer to Problem 25A

The value of 75.2 cal in joule is $\text{314}\text{.64}\text{J}$ and in kilojoules is $314.64\times {10}^{-3}\text{kJ}$ .

Explanation of Solution

Convert 75.2 cal into joules:

Since,

  $\begin{array}{c}\text{1cal=4}\text{.184}\text{J}\\ \text{75}\text{.2}\text{cal=}\frac{\text{75}\text{.2}\text{cal}\times \text{4}\text{.184}\text{J}}{\text{1cal}}\\ \text{=314}\text{.64}\text{J}\end{array}$

Therefore, convert $314.64\text{J}$ into kilojoules as follows:

  $\begin{array}{c}75.2\text{cal}\times \frac{\text{4}\text{.184}\text{J}}{\text{1}\text{cal}}=314.64\text{J}\times \frac{1\text{kJ}}{{10}^3\text{J}}\\ =314.64\times {10}^{-3}\text{kJ}\end{array}$

(c)

Interpretation Introduction

Interpretation: Conversion of $1.41\times {10}^3$ cal to joules and kilojoules needs to be explained.

Concept Introduction: In metric system, Calorie is the amount of energy (heat) required to increase 1 g of water by $1\text{°C}$ . The conversion factor used to convert calories into joules is $\frac{\text{4}\text{.184J}}{\text{1}\text{cal}}$ and conversion of kcal into kilojoules is $\frac{\text{4}\text{.184}\text{kJ}}{\text{1}\text{kcal}}$ .

Answer to Problem 25A

The value of $1.41\times {10}^3$ cal in joule is $\text{5}\text{.90}\times {\text{10}}^3\text{J}$ and in kilojoules is $5.90\text{kJ}$ .

Explanation of Solution

Convert $1.41\times {10}^3$ cal into joules:

Since,

  $\begin{array}{c}\text{1cal=4}\text{.184}\text{J}\\ \text{1}\text{.41}\times {\text{10}}^3\text{cal=}\frac{\text{1}\text{.41}\times {\text{10}}^3\text{cal}\times \text{4}\text{.184}\text{J}}{\text{1cal}}\\ \text{=5}\text{.90}\times {\text{10}}^3\text{J}\end{array}$

Therefore, convert $\text{5}\text{.90}\times {\text{10}}^3\text{J}$ into kilojoules as follows:

  $\begin{array}{c}1.41\times {10}^3\text{cal}\times \frac{\text{4}\text{.184}\text{J}}{\text{1}\text{cal}}=5.90\times {10}^3\text{J}\times \frac{1\text{kJ}}{{10}^3\text{J}}\\ =5.90\text{kJ}\end{array}$

(d)

Interpretation Introduction

Interpretation: Conversion of 1.41 kcal to joules and kilojoules needs to be explained.

Concept Introduction: In metric system, Calorie is the amount of energy (heat) required to increase 1 g of water by $1\text{°C}$ . The conversion factor used to convert calories into joules is $\frac{\text{4}\text{.184J}}{\text{1}\text{cal}}$ and conversion of kcal into kilojoules is $\frac{\text{4}\text{.184}\text{kJ}}{\text{1}\text{kcal}}$ .

Answer to Problem 25A

The value of 1.41kcal in joule is $\text{5899}\text{.4}\text{J}$ and in kilojoules is $5.90\text{kJ}$ .

Explanation of Solution

Convert 1.41 kcal into joules:

  $\begin{array}{c}\text{1}\text{kcal=1000}\text{cal}\\ 1.41\text{kal=1}\text{.41×1000}\text{cal}\\ \text{=1410}\text{cal}\end{array}$

Since,

  $\begin{array}{c}\text{1cal=4}\text{.184}\text{J}\\ \text{1410}\text{cal=}\frac{\text{1410}\text{cal}\times \text{4}\text{.184}\text{J}}{\text{1cal}}\\ \text{=5899}\text{.4}\text{J}\end{array}$

Conversion factor for kilocalories to kilojoules is $\frac{\text{4}\text{.184}\text{kJ}}{\text{1}\text{kcal}}$ .

Therefore, convert 1.41 kcal into kilojoules as follows:

  $1.41\text{kcal}\times \frac{\text{4}\text{.184}\text{kJ}}{\text{1}\text{kcal}}=5.90\text{kJ}$