Chapter 6, Problem 6.99P

(a)

Interpretation Introduction

Interpretation:

The mass of known deposits of natural gas is to be calculated.

Concept introduction:

Mass is a physical quantity and its SI unit is kilograms $\left(\text{kg}\right)$. It is the measure of the quantity of the matter present in an object. The other units of mass are grams, milligrams.

The conversion of one unit into another can be done using a proper conversion factor. Conversion factors are the ratios that relate the two different units of a quantity. It is also known as dimensional analysis or factor label method.

In the unit conversion problems, the given information is multiplied by the conversion factors to obtain the desired information. The unit conversion can be done as follows:

  $\left(\cancel{\text{beginning unit}}\right)\left(\frac{\text{Final unit}}{\cancel{\text{beginning unit}}}\right)=\text{Final unit}$

The conversion factor to convert $\text{EJ}$ into $\text{J}$ is:

  $\text{1}\text{EJ}={10}^{18}\text{J}$

(b)

Interpretation Introduction

Interpretation:

The number of years could these deposits supply the world’s total energy needs is to be calculated.

Concept introduction:

The conversion of one unit into another can be done using a proper conversion factor. Conversion factors are the ratios that relate the two different units of a quantity. It is also known as dimensional analysis or factor label method.

In the unit conversion problems, the given information is multiplied by the conversion factors to obtain the desired information. The unit conversion can be done as follows:

  $\left(\cancel{\text{beginning unit}}\right)\left(\frac{\text{Final unit}}{\cancel{\text{beginning unit}}}\right)=\text{Final unit}$

(c)

Interpretation Introduction

Interpretation:

The volume of natural gas required to heat $1.00\text{ qt}$ of water is to be calculated.

Concept introduction:

Specific heat capacity $\left(c\right)$ of a substance is the amount of heat needed to raise the temperature of $1\text{g}$ of a substance by $1\text{K}$. The formula to calculate heat required is as follows:

  $q=\left(\text{mass}\right)\left(c\right)\left(T_2-T_1\right)$        (1)

Here,

$T_2$ is the final temperature.

$T_1$ is the initial temperature.

$q$ is the heat released or absorbed.

$c$ is the specific heat capacity of the substance.

Density is defined as mass per unit volume. Mass and volume are physical quantities and the units of mass and volume are fundamental units. Density is the ratio of mass to the volume. The unit of volume is derived from the units of mass and volume. The SI unit of density is ${\text{kg/m}}^{\text{3}}$. The formula to calculate density is,

  $\text{Density}=\frac{\text{Mass}}{\text{Volume}}$        (2)

The conversion factor to convert $\text{qt}$ to $\text{L}$ is as follows:

  $1\text{L}=1.057\text{qt}$

The formula to calculate mass of a substance is as follows:

  $\text{Mass of a substance}=\left(\text{Moles}\right)\left(\text{molar mass}\right)$        (3)

(d)

Interpretation Introduction

Interpretation:

The volume of natural gas would produce $2\times {10}^{13}\text{J}$ of energy is to be calculated.

Concept introduction:

Density is defined as mass per unit volume. Mass and volume are physical quantities and the units of mass and volume are fundamental units. Density is the ratio of mass to the volume. The unit of volume is derived from the units of mass and volume. The SI unit of density is ${\text{kg/m}}^{\text{3}}$. The formula to calculate density is,

  $\text{Density}=\frac{\text{Mass}}{\text{Volume}}$        (2)