Chapter 9, Problem 9.1YT

Conversion of Energy Units

The complete combustion of a small wooden match produces approximately 512 cal of heat. How many kilojoules (kJ) are produced?

Interpretation Introduction

Interpretation:

The heat (in kilojoules) that is produced during the complete combustion of a small wooden match is to be determined.

Concept introduction:

Unit conversion is defined as the process in which multiple steps are used to convert the unit of measurement of the same given quantity.

Answer to Problem 9.1YT

Solution: $2.14\text{ kJ}$

Explanation of Solution

Given information: The complete combustion of a small wooden match produces approximately $512\text{ cal}$ of heat.

As it is known, one calorie is equal to $4.18\text{ J}$. Therefore, it can be written as:

$1\text{ cal}=\text{4}\text{.18 J}$

Conversion factor cal to joul is as:

$\frac{\text{4}\text{.18 J}}{1\text{ cal}}$

The amount of heat produced by combusting a small wooden match is $512\text{ cal}$ can be converted in joules as follows:

$\begin{array}{c}\text{Heat}=512\cancel{\text{cal}}\times \frac{\text{4}\text{.18 J}}{1\cancel{\text{cal}}}\\ =\text{2140}\text{.16 J}\\ =\text{2}\text{.14}\times {\text{10}}^3\text{ J}\end{array}$

As it is known, 1 kilojoule is 1000 joules, hence conversion factor is as:

$\frac{1\text{kJ}}{{10}^3\text{J }}$

For converting heat into kilojoules, it is divided by ${10}^3$ as follows:

$\begin{array}{c}2.14\times {10}^3\text{ J}=\text{2}\text{.14}\times \cancel{{10}^3\text{J}}\frac{1\text{kJ}}{\cancel{{10}^3\text{J}}}\\ =\text{2}\text{.14 kJ}\end{array}$

Conclusion

During the complete combustion of a small wooden match, $2.14\text{ kJ}$ heat will be produced.