Chapter 6, Problem 6.98P

(a)

Interpretation Introduction

Interpretation:

The joules are in $1.00\text{ Btu}$ is to be calculated.

Concept introduction:

The calorie $\left(4.184\text{J}\right)$ is defined as the amount of energy required to increase the temperature of $1.00\text{ g}$ of liquid water by $1.00°\text{C}$. The British thermal unit is defined as the amount of energy required to increase the temperature of $1.00\text{ lb}$ of liquid water by $1.00°\text{F}$.

The conversion factor to convert $\text{lb}$ into $\text{g}$ is:

  $\text{1}\text{lb}=453.6\text{g}$

The conversion factor to convert $°\text{C}$ into $°\text{F}$ is:

  $\text{1}°\text{C}=1.8°\text{F}$

(b)

Interpretation Introduction

Interpretation:

The joules in $1.00\text{ therm}$ is to be calculated.

Concept introduction:

The calorie $\left(4.184\text{J}\right)$ is defined as the amount of energy required to increase the temperature of $1.00\text{ g}$ of liquid water by $1.00°\text{C}$. The British thermal unit is defined as the amount of energy required to increase the temperature of $1.00\text{ lb}$ of liquid water by $1.00°\text{F}$.

The conversion factor to convert $\text{therm}$ into $\text{btu}$ is:

  $\text{1}\text{therm}=100,000\text{btu}$

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

  $\text{1}\text{btu}=1054.368\text{J}$

(c)

Interpretation Introduction

Interpretation:

The mole of methane that must be burned to give $1.00 \text{therm}$ of energy is to be calculated.

Concept introduction:

The standard enthalpy of reaction is calculated by the summation of standard enthalpy of formation of the product minus the summation of standard enthalpy of formation of reactant at the standard conditions. The formula to calculate the standard enthalpy of reaction $\left(\Delta H_{\text{rxn}}^{°}\right)$ is as follows:

  $\Delta H_{\text{rxn}}^{°}=\sum m\Delta H_{\text{f (products)}}^{°}-\sum n\Delta H_{\text{f (reactants)}}^{°}$

Here, m and n are the stoichiometric coefficients of reactants and product in the balanced chemical equation.

(d)

Interpretation Introduction

Interpretation:

The cost per mole of methane is to be calculated.

Concept introduction:

The calorie $\left(4.184\text{J}\right)$ is defined as the amount of energy required to increase the temperature of $1.00\text{ g}$ of liquid water by $1.00°\text{C}$. The British thermal unit is defined as the amount of energy required to increase the temperature of $1.00\text{ lb}$ of liquid water by $1.00°\text{F}$.

(e)

Interpretation Introduction

Interpretation:

The cost to warm $\text{318 gal}$ of water in a hot tub from $15.0°\text{C}$ to $42.0°\text{C}$ 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:

  $q=\left(\text{mass}\right)\left(c\right)\left(T_2-T_1\right)$        (2)

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,

  $\text{Density}=\frac{\text{Mass}}{\text{Volume}}$        (3)

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

  $1\text{gal}=4\text{qt}$

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

  $1\text{L}=1.057\text{qt}$