Chapter 1, Problem 45E

Precious metals and gems are measured in troy weights in the English system:

24 grains 1 pennyweight (exact)

20 pennyweight = 1 troy ounce (exact)

12 troy ounces 1 troy pound (exact)

1 grain = 0.0648 g

1 carat = 0.200 g

1. a. The most common English unit of mass is the pound avoirdupois. What is 1 troy pound in kilograms and in pounds?
2. b. What is the mass of a troy ounce of gold in grams and in carats?
3. c. The density of gold is 19.3 g/cm³. What is the volume of a troy pound of gold?

Interpretation Introduction

Interpretation:

Unit conversion for the given value have to be given.

Answer to Problem 45E

1 troy pound weight in kilogram is $\text{0}\text{.3732}\text{kg,}$1 troy pound in pounds is $\text{0}\text{.8228}\text{pounds}\text{.}$

Explanation of Solution

To calculate: 1 troy pound weight in kilograms and pounds

1 troy pound weight in kilograms and pounds is calculated below

Given conversion factors:

$\begin{array}{l}\text{24 grains = 1 pennyweight }\left(\text{exact}\right)\\ \text{20 pennyweight = 1 troy ounce }\left(\text{exact}\right)\\ \text{12 troy ounces = 1 troy pound }\left(\text{exact}\right)\\ \text{1 grain = 0}\text{.0648}\text{g}\\ \text{I carat = 0}\text{.200 g}\end{array}$

Apply the unit conversion factor and given data to calculate the weight of 1 troy pound in kilograms

$\begin{array}{l}\text{1}\text{×}\text{10}{}^{\text{3}}\text{g}\text{=}\text{1}\text{kg}\\ \text{1}\text{kg}\text{=}\text{2}\text{.2046}\text{pounds}\end{array}$

$\begin{array}{l}\text{1}\text{troy}\text{pound}\text{×}\frac{\text{0}\text{.0648}\text{g}}{\text{1}\text{grain}}\text{×}\frac{\text{24}\text{grains}}{\text{1}\text{penny}\text{weight}}\text{×}\frac{\text{20}\text{penny}\text{weight}}{\text{1}\text{troy}\text{ounce}}\text{×}\frac{\text{12}\text{troy}\text{ounces}}{\text{1}\text{troy}\text{pound}}\text{=}\text{373}\text{.}\text{248}\text{g}\\ \text{=}\text{373}\text{.248}\text{g}\text{×}\frac{\text{1}\text{kg}}{\text{1}\text{×}{\text{10}}^{\text{3}}\text{g}}\\ \text{=}\text{0}\text{.3732}\text{kg}\end{array}$

Apply the unit conversion factor to calculate 1 troy pound weight in pounds

$\text{0}\text{.3732}\text{kg}\text{×}\frac{\text{2}\text{.2046}\text{pounds}}{\text{1}\text{kg}}\text{=}\text{0}\text{.8228}\text{pounds}$

Interpretation Introduction

Interpretation:

Unit conversion for the given value have to be given.

Answer to Problem 45E

The mass of 1 troy ounce of gold in grams is $\text{31}\text{.104}\text{g,}$ in carats is $\text{155}\text{.52}\text{carats}\text{.}$

Explanation of Solution

To calculate: the weight of 1 troy ounce of gold in grams and carats

1 troy ounce of gold in grams and carats is calculated below

Apply the unit conversion factor and given data to calculate the 1 troy ounce weight in grams

$\begin{array}{l}\text{1}\text{troy}\text{ounce}\text{×}\frac{\text{0}\text{.0648}\text{g}}{\text{1}\text{grain}}\text{×}\frac{\text{24}\text{grains}}{\text{1}\text{penny}\text{weight}}\text{×}\frac{\text{20}\text{penny}\text{weight}}{\text{1}\text{troy}\text{ounce}}\\ \text{=}\text{31}\text{.104}\text{g}\end{array}$

Apply the unit conversion factor and given data to calculate the 1 troy ounce weight in carats

$\begin{array}{l}\text{General}\text{unit}\text{conversion}\\ \text{1}\text{gram}\text{=}\text{5}\text{carats}\end{array}$

$\text{31}\text{.104}\text{g}\text{×}\frac{\text{5}\text{carats}}{\text{1}\text{g}}\text{=}\text{155}\text{.}\text{52}\text{carats}$

Interpretation Introduction

Interpretation:

Unit conversion for the given value have to be given.

Answer to Problem 45E

The volume of a troy pound of gold is $\text{19}\text{.339}{\text{cm}}^{\text{3}}\text{.}$

Explanation of Solution

To calculate: the volume of a troy pound of gold

The volume of a troy pound of gold is calculated below

Given data:

$\text{density}\text{of}\text{gold}\text{is}\text{19}\text{.3}\raisebox{1ex}{$\text{g}$}\!\left/ \!\raisebox{-1ex}{${\text{cm}}^{\text{3}}$}\right.$

Relationship between density and volume is given by

$\begin{array}{l}\text{d}\text{=}\frac{\text{m}}{\text{V}}\\ \text{d-}\text{density;}\text{m-}\text{mass;}\text{V-}\text{volume}\end{array}$

The mass of 1 troy pound in gram unit is $\text{373}\text{.248}\text{g}$

Calculate the volume of the troy pound of gold

$\begin{array}{l}\text{modified density equation is given by}\\ \text{V}\text{=}\frac{\text{m}}{\text{d}}\\ \text{V=}\frac{\text{373}\text{.248}\text{g}}{\text{19}\text{.3}\raisebox{1ex}{$\text{g}$}\!\left/ \!\raisebox{-1ex}{${\text{cm}}^{\text{3}}$}\right.}\text{=}\text{19}\text{.339}{\text{cm}}^{\text{3}}\end{array}$