Environmental Engineering Reference
In-Depth Information
chemical energy from liquid fuel, converts it into mechani-
cal energy, which is transferred to the coolant and then
radiator as heat energy, which transfers it to the atmosphere.
Moreover, sunlight hitting a paved parking lot gets trans-
ferred into heat, whereas the same sunlight hitting the leaf of
a plant is, in part, stored as energy in compounds made by
the plant.
The second law of thermodynamics states that the disor-
der of a system, or entropy, always increases or entropy is
not conserved. For example, using photosynthesis,
converting simple molecules, like CO 2 and H 2 O, into more
complex organic molecules may decrease the entropy of the
plant initially, going from disorder to order, but this is more
than balanced by the increase in entropy that results from the
input of solar energy.
The exchange of energy from one compartment to
another can take two forms—heat and work. In the example
of the internal combustion engine, the chemical energy in
the fuel is exchanged into the mechanical energy of the
pistons moving in the cylinders to turn a crankshaft.
Hence, the fuel energy is converted into both heat and
work. Work can be defined as force multiplied by the dis-
tance covered by the force or against a resisting force.
Water also contains a certain level of energy inherent to
its atoms and bonds of its molecular structure. Water
molecules in motion can exchange this energy with their
surroundings, such as a cell wall. The speed of molecular
motion is what determines the magnitude of its energy. At
normal temperatures and pressures, the ability of molecular
interaction to occur spontaneously is referred to as Gibbs
free energy, after work done by J.W. Gibbs in the 1930s
(Kramer and Boyer 1995). This free energy is proportional
to the number of molecules on a free energy per mole basis
and can be called chemical-free energy, or chemical poten-
tial, u . This potential is essentially a measure of the tendency
of a chemical to undergo transformation, or the potential
energy state of a chemical. Water, for example, can be
evaporated, advected, or diffused.
Because u is not an absolute, an interesting aspect of
chemical potential is the difference between the u of an
initial and final state. If the difference is negative, the change
occurs; if the difference is positive, or zero, no change
occurs. Zero chemical potential represents the system at
equilibrium. For example, the conversion of liquid water
into gaseous hydrogen and oxygen does not occur spontane-
ously because the change in u is positive. But how then, can
we explain the similar conversion of liquid water into gas-
eous oxygen during photosynthesis? Although the hydrogen
is used to reduce CO 2 , the primary driving force to overcome
the increase in u is provided by solar energy.
The chemical potential, or free energy, of water that
arises from the random movement of water molecules in
contact with each other will change if temperature or
pressure changes. As might be expected, boiling water that
releases water vapor causes the chemical potential to
increase because of the increased force at which water
molecules collide with each other. The same conversion
process that turns water to vapor also occurs in evaporation
and transpiration, although the chemical potential is lower
because of lower temperatures. Similarly, increased pressure
also causes the chemical potential of water to increase as if
the temperature has increased, because the water molecules
are so tightly packed together—this is why squeezing an ice
cube can cause it to rapidly melt.
For a sample of pure liquid water at 1 atm (1 bar) and
20 C, the reference standard for u is arbitrarily assigned as
u o ¼
0 Megapascals (0 MPa). This value is the highest water
potential possible, by definition, so all other potentials will
be a negative number less than zero, because differences in
water potential are more useful than actual values. The more
negative a value of u is for water in soil, for example, the
lower is the energy state and more energy is required to
remove water from soil, where the energy ultimately is
derived from the sun.
The unknown u , u w , of water can be compared to the
standard,
u w
u o :
(3.14)
When u w is pure water,
u w
u o ¼
0
:
(3.15)
As previously discussed, the chemical potential of water
can be increased by increasing temperature and pressure. On
the other hand, the chemical potential of water can be
decreased by the reverse—decreasing temperature and pres-
sure—or by adding a solute to the water to form a solution.
When u w is not pure water, as is the case when a solute is
added and the number of molecules of water decreases, or,
the presence of the solute molecules, which often are larger
than the water molecules, interferes with water molecule
movement, the end result is that the chemical potential of
water, u w , decreases
u w
u o ¼
a negative number
:
(3.16)
The negative number indicates that the movement of
water would occur spontaneously from a less negative
(water with less solute), to a more negative number (water
with more solute).
The units of chemical potential are energy units/mole,
or Joules/mole. To convert to pressure, in the case of water,
the chemical potential can be converted to a water potential,
c
, by normalizing the difference in chemical potential
by the partial molar volume of water ( V ,inm 3 /mole), or
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