First Principles - Sustainable Design: The Science of Sustainability and Green Engineering - page 52

change the elevation of the body:

W = E potential (2.4)

The work-energy principle states that in keeping with the conservation law (recall
the first law of thermodynamics), external work that is performed on a system
will go into changing the system's total energy:

W = E = E 2 − E 1 (2.5)

This principle is generally limited to mechanical energy relationships.
We can see these mass-energy-work relationships in solving a few example
problems.

Green Physics Example 1 Calculate the work done by 4 million kilograms
of effluent pumped from a sluice gate into a holding pond if the water starts
from rest, accelerates uniformly to a constant stream velocity of 1 m s − 1 , then
decelerates uniformly to stop 2 m higher than the initial position in the sluice.
Neglect friction and other losses.

Solution Applying the work-energy principle, the work done on the effluent
is equal to the change in the effluent's energy. Since the initial and final kinetic
energy is zero (i.e., the effluent starts at rest and stops again), the only change in
mechanical energy is the change in potential energy. Using the initial elevation
of the effluent as the reference height (i.e., h 1 = 0), then

10 6 )(9 81m s − 2 )(2m) W = E 2potential − E 1potential = mg ( h 2 − h 1 ) = (4 × .

10 7 J = 7 . 85 ×

Converting one energy form to another is in keeping with the conservation
law. Most conversions are actually special cases of the work-energy principle. If
a falling body is acted on by gravity, for example, the conversion of potential
energy into kinetic energy is really just a way of equating the work done by the
gravitational force (constant) to the change in kinetic energy. Joule's law states
that one energy form can be converted to another energy form without loss.
Regarding thermodynamic applications, Joule's law says that the internal energy
of an ideal 1 gas is a function of the temperature change, not of the change in
volume.