Chapter 20, Problem 54RQ

Interpretation Introduction

Interpretation:

The energy equivalent of a mass of $1.00\text{ g}$ in $\text{kJ}$ is to be determined.

Concept Introduction:

When mass is converted to energy, relation between the change in energy and the change in rest mass is given by Einstein equation as follows:

$\Delta E=\Delta m_{\circ }{\text{c}}^{\text{2}}$

Here, $\Delta \text{E}$ is the change in energy, $\Delta \text{m}$ is the change in rest mass and $\text{c}$ is the velocity of light $\left(3.00\times {10}^8{\text{ ms}}^{-1}\right)$.

Conversion of kJ to J is done with the help of following relationship,

$\text{1 kJ = }1.00\times {\text{10}}^3\text{J}$

Conversion factor is

$\frac{1.00\times {\text{10}}^3\text{J}}{\text{1 kJ}}$

Conversion of J to ${\text{kgm}}^2{\text{s}}^{-2}$ is done with the help of following relationship,

$1\text{ J = }1{\text{kgm}}^2{\text{s}}^{-2}$

Conversion factor is

$\frac{1{\text{kgm}}^2{\text{s}}^{-2}}{1\text{J}}$

Conversion of g to kg is done with the help of following relationship,

$\text{1 kg = }{10}^3\text{g}$

Conversion factor is

$\frac{{10}^3\text{g}}{1\text{ kg}}$