Chapter 1, Problem 1.36P

(a)

Interpretation Introduction

Interpretation:

SI unit conversion has to be performed for $\text{1}\text{.259}\times {\text{10}}^{\text{3}}\text{J}$ to $\text{kJ}$.

Concept Introduction:

Conversion of one unit into another unit is done by the use of unit conversion factor.  This involves multiplying or dividing by the power of 10.  For example, if centimeter has to be converted into meter, then the given value in centimeter has to be multiplied by the conversion factor as shown below.

    $1=\frac{1\text{m}}{100\text{cm}}$

Explanation of Solution

Given value is $\text{1}\text{.259}\times {\text{10}}^{\text{3}}\text{J}$.  This has to be converted into kilojoules using the conversion factor.  Conversion factor for joules and kilojoules conversion is given below.

    $\frac{1\text{kJ}}{100\text{0}\text{J}}or\frac{1000\text{J}}{1\text{kJ}}$

As the given value is in joules, the first conversion factor is considered.  The SI unit conversion is performed as shown below.

    $\text{1}\text{.259}\times {\text{10}}^{\text{3}}\text{J}\times \frac{1\text{kJ}}{100\text{0}\text{J}}=1.259\text{kJ}$

Therefore, the SI unit converted value of $\text{1}\text{.259}\times {\text{10}}^{\text{3}}\text{J}$ is $1.259\text{kJ}$.

(b)

Interpretation Introduction

Interpretation:

SI unit conversion has to be performed for $\text{2}\text{.18}\times {\text{10}}^{\text{-18}}\text{J}$ to $\text{aJ}$.

Concept Introduction:

Refer part (a).

Explanation of Solution

Given value is $\text{2}\text{.18}\times {\text{10}}^{\text{-18}}\text{J}$.  This has to be converted into attojoules using the conversion factor.  Conversion factor for joules and attojoules conversion is given below.

    $\frac{1\text{aJ}}{{10}^{-18}\text{J}}or\frac{{10}^{-18}\text{J}}{1\text{aJ}}$

As the given value is in joules, the first conversion factor is considered.  The SI unit conversion is performed as shown below.

    $\text{2}\text{.18}\times {\text{10}}^{\text{-18}}\text{J}\times \frac{1\text{aJ}}{{10}^{-18}\text{J}}=2.18\text{aJ}$

Therefore, the SI unit converted value of $\text{2}\text{.18}\times {\text{10}}^{\text{-18}}\text{J}$ is $2.18\text{aJ}$.

(c)

Interpretation Introduction

Interpretation:

SI unit conversion has to be performed for $\text{5}\text{.5}\text{MJ}$ to $\text{kJ}$.

Concept Introduction:

Refer part (a).

Explanation of Solution

Given value is $\text{5}\text{.5}\text{MJ}$.  This has to be converted into kilojoules using the conversion factor.  Conversion factor for megajoules and kilojoules conversion is given below.

    $\begin{array}{c}\frac{1\text{kJ}}{1000\text{J}}or\frac{1000\text{J}}{1\text{kJ}}\\ \text{and}\\ \frac{1\text{MJ}}{1000000\text{J}}or\frac{1000000\text{J}}{1\text{MJ}}\end{array}$

As the given value is in megajoules, the conversion is done using the conversion factors as shown below.

    $\begin{array}{c}\text{5}\text{.5}\text{MJ}\times \frac{1000000\text{J}}{1\text{MJ}}\times \frac{1\text{kJ}}{1000\text{J}}=\frac{5.5\times {10}^6}{{10}^3}\text{kJ}\\ \text{=5}\text{.5}\times {\text{10}}^{\text{3}}\text{kJ}\end{array}$

Therefore, the SI unit converted value of $\text{5}\text{.5}\text{MJ}$ is $\text{5}\text{.5}\times {\text{10}}^{\text{3}}\text{kJ}$.

(d)

Interpretation Introduction

Interpretation:

SI unit conversion has to be performed for $\text{7}\text{.5}\times {\text{10}}^{\text{-3}}\text{ns}$ to $\text{fs}$.

Concept Introduction:

Refer part (a).

Explanation of Solution

Given value is $\text{7}\text{.5}\times {\text{10}}^{\text{-3}}\text{ns}$.  This has to be converted into femtosecond using the conversion factor.  Conversion factor for nanosecond and femtosecond conversion is given below.

    $\begin{array}{c}\frac{1\text{ns}}{{10}^{-9}\text{s}}or\frac{{10}^{-9}\text{s}}{1\text{ns}}\\ \text{and}\\ \frac{1\text{fs}}{{10}^{-15}\text{s}}or\frac{{10}^{-15}\text{s}}{1\text{fs}}\end{array}$

As the given value is in nanoseconds, the conversion to femtosecond can be done as shown below using conversion factors.

    $\begin{array}{c}\text{7}\text{.5}\times {\text{10}}^{\text{-3}}\text{ns}\times \frac{{10}^{-9}\text{s}}{1\text{ns}}\times \frac{1\text{fs}}{{10}^{-15}\text{s}}=\frac{7.5\times {10}^{-12}\text{fs}}{{10}^{-15}}\\ =7.5\times {10}^3\text{fs}\end{array}$

Therefore, the SI unit converted value of $\text{7}\text{.5}\times {\text{10}}^{\text{-3}}\text{ns}$ is $7.5\times {10}^3\text{fs}$.

(e)

Interpretation Introduction

Interpretation:

SI unit conversion has to be performed for $\text{2}\text{.0}{\text{m}}^{\text{3}}$ to $\text{mL}$.

Concept Introduction:

Refer part (a).

Explanation of Solution

Given value is $\text{2}{\text{.0 m}}^{\text{3}}$.  This has to be converted into milliliter using the conversion factor.  Conversion factor for cubicmeter and milliliter conversion is given below.

    $\frac{1{\text{m}}^{\text{3}}}{{10}^6\text{mL}}or\frac{{10}^6\text{mL}}{1{\text{m}}^{\text{3}}}$

As the given value is in cubicmeter, the second conversion factor is used.  This is performed as shown below.

    $\text{2}{\text{.0 m}}^{\text{3}}\times \frac{{10}^6\text{mL}}{1{\text{m}}^{\text{3}}}=\text{2}\times {10}^6\text{mL}$

Therefore, the SI unit converted value of $\text{2}\text{.0}{\text{m}}^{\text{3}}$ is $\text{2}\times {10}^6\text{mL}$.