Book edition 9th Edition

Author(s) Raymond A. Serway, John W. Jewett

Pages 1624 pages

ISBN 9781133947271

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Short Answer

A solid piece of lead has a mass of $23.94 g$ and a volume of $2.10 {cm}^{3}$ .From these data, calculate the density of lead in SI units (kilograms per cubic meter).

The density of the solid piece of lead in SI unit is $11.4 \times 10^{3} {kg/m}^{3} .$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1:Definition and units of density of a substance

The amount of mass of any substance to its quantity or volume gives the density of that substance. Density is defined as the ratio of a mass to the volume of asubstance.

Density is measured inSI unit— $kg / m^{3}$ andCGS unit— $g / {cm}^{3}$

Unit conversion is a conversion of a unit of the same quantity from one unit to another using multiplication or division. It is a multistep process that involves multiplication/division by conversion factor

Step 2: Expression for the density of a substance and unit conversion

Write the expression for the density of the lead substance in terms of its mass and volume.

$ρ = \frac{m}{V} \dots \dots (1)$

Here, $ρ$ is the density of the lead, $m$ is mass of the lead, and $V$ is volume of the lead.

Unit conversion method is used for the density measurements so that the final result will be close to the expected value.

Convert the unit $2.10 {cm}^{3}$ for volume $V$ to $m^{3}$ .

$\begin{array}{rcl} {cm}^{3} & = & 1 \times 10^{- 6} m^{3} \\ 2.10 {cm}^{3} & = & 2.10 \times 10^{- 6} m^{3} \end{array}$

Convert the unit $23.94 g$ for mass $m$ to $k g$ .

localid="1663589234857" $\begin{array}{rcl} 1 {g = 10}^{- 3} kg \\ 23.94 g = 23.94 \times 10^{- 3} kg \end{array}$

Step 3: Calculation of density of solid piece of lead in SI units

Replace $23.94 \times 10^{- 3} kg$ for $m$ and $2.10 \times 10^{- 6} m^{3}$ for $V$ in equation (1).

$\begin{array}{rcl} d ρ & = & \frac{23.94 \times 10^{- 3} kg}{2.10 \times 10^{- 6} m^{3}} \\ = & 11.4 \times 10^{3} {kg/m}^{3} . \end{array}$

Hence, the density of the $ρ$ of the solid piece of lead is $11.4 \times 10^{3} {kg/m}^{3} .$

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Physics For Scientists & Engineers

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Short Answer

A solid piece of lead has a mass of $23.94 g$ and a volume of $2.10 {cm}^{3}$ .From these data, calculate the density of lead in SI units (kilograms per cubic meter).

Step by Step Solution

Step 1:Definition and units of density of a substance

Step 2: Expression for the density of a substance and unit conversion

Step 3: Calculation of density of solid piece of lead in SI units

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Physics For Scientists & Engineers

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Short Answer

A solid piece of lead has a mass of 23.94 gand a volume of 2.10 cm3.From these data, calculate the density of lead in SI units (kilograms per cubic meter).

Step by Step Solution

Step 1:Definition and units of density of a substance

Step 2: Expression for the density of a substance and unit conversion

Step 3: Calculation of density of solid piece of lead in SI units

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A solid piece of lead has a mass of $23.94 g$ and a volume of $2.10 {cm}^{3}$ .From these data, calculate the density of lead in SI units (kilograms per cubic meter).