Chapter 1, Problem

(a)

To determine

Determine the energy associated while dropping the coal from the given height.

Answer

The energy associated while dropping the coal is $\underset{\_}{980\text{J}}$.

Explanation of Solution

Given information:

Mass of the coal is $m=1\text{kg}$.

Vertical height is $h=100\text{m}$.

Calculation:

Refer Appendix II, “Physical constants” for gravitational acceleration value in the textbook.

The value of gravitational acceleration is $g=9.8{\text{m/s}}^{\text{2}}$.

Find the potential energy associated due to gravitation using the relation:

$\begin{array}{c}E=mgh\\ =\left(1\text{kg}\right)\left(9.8{\text{m/s}}^{\text{2}}\right)\left(100\text{m}\right)\\ =980\text{J}\end{array}$

Therefore, the energy associated while dropping the coal is $\underset{\_}{980\text{J}}$.

(b)

To determine

Determine the energy associated while burning the coal.

Answer

The energy associated while burning the coal is $\underset{\_}{3.28\times {10}^7\text{J}}$.

Explanation of Solution

Given information:

Mass of the coal is $m=1\text{kg}$.

Calculation:

Let consider the coal contains 100% of carbon.

Refer Equation (1.13) in the textbook.

Combustion of 1 kg of carbon releases energy of $E=32.8\text{MJ}$.

Convert 32.8 MJ into J:

$\begin{array}{c}E=32.8\text{MJ}\times \frac{{10}^6\text{J}}{\text{MJ}}\\ =3.28\times {10}^7\text{J}\end{array}$

Therefore, the energy associated while burning the coal is $\underset{\_}{3.28\times {10}^7\text{J}}$.

(c)

To determine

Determine the energy associated while converting the mass of the coal into energy.

Answer

The energy associated while converting the mass of the coal into energy is $\underset{\_}{9\times {10}^{16}\text{J}}$.

Explanation of Solution

Given information:

Mass of the coal is $m=1\text{kg}$.

Calculation:

Refer Appendix II, “Physical constants” for speed of light value in the textbook.

The value of speed of light is $c=3\times {10}^8\text{m/s}$.

Find the energy associated using the relation:

$\begin{array}{c}E=m{c}^2\\ =\left(1\text{kg}\right){\left(3\times {10}^8\text{m/s}\right)}^2\\ =9\times {10}^{16}\text{J}\end{array}$

Therefore, the energy associated while converting the mass of the coal into energy is $\underset{\_}{9\times {10}^{16}\text{J}}$.

Compare the energy scale level for the three cases as follows:

The mass of energy while converting the mass $\left(9\times {10}^{16}\text{J}\right)$ has higher order of magnitude compared to the energy forms due to dropping and burning.

The energy due to burning $\left(3.28\times {10}^7\text{J}\right)$ is approximately greater than 30, 000 times the energy associated due to gravitation $\left(980\text{J}\right)$.