Chapter 1, Problem 1P

(a)

To determine

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

Answer to Problem 1P

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 to Problem 1P

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 to Problem 1P

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 $\left(980\text{J}\right)$.