Compare the energy scales of mechanical, chemical, and mass energy by calculating (a) the energy associated with dropping 1 kg of coal through a vertical distance of 100 m, (b) burning 1 kg of coal, and (c) converting the mass of 1 kg of coal into energy.

Question

Quizplus · Accepted Answer

The Answer is (a) The gravitational potential energy is given as

E = m g h = ( 1 \mathrm {~kg} ) imes \left( 9.8 \frac { \mathrm { m } } { \mathrm { s } ^ { 2 } } ight) imes ( 100 \mathrm {~m} ) = 980 \mathrm {~J}

(b) Assuming coal is

\sim 100 \%

carbon from equation (1.10)

1 \mathrm {~kg}

coal yields

32.8 \mathrm { MJ } = 3.28 imes 10 ^ { 7 } \mathrm {~J}

.
(c) From the Einstein relation

E = m c ^ { 2 } = ( 1 \mathrm {~kg} ) imes \left( 3 imes 10 ^ { 8 } \frac { \mathrm { m } } { \mathrm { s } } ight) ^ { 2 } = 9 imes 10 ^ { 16 } \mathrm {~J}

These values emphasize the relative magnitudes of mechanical, chemical and mass energy.While it may not be surprising that the mass energy is many orders of magnitude greater than the other forms of energy, it is interesting to note that the chemical energy is more than 30,000 times the gravitational energy in this example.

Compare the Energy Scales of Mechanical, Chemical, and Mass Energy