Work.
If an open system is necessary, what other factors do we need to
consider in addition to an open system? In our previous example, we
simply considered an open system with heat flowing through it. Heat
(q) is one component that can be related to E in the following way:
DE = q + w, where (+)w = work done on the system by the surroundings
(the first law). Thus, the change in energy of a system can be said
to consist of two energy components, heat and work. Connecting this
to living systems, an open system is necessary for life, but not
sufficient - mass and energy flowing through the system must be
coupled to this second component, work. An open system with energy
flowing from the surroundings to the system satisfies the condition
of being capable of doing work on the system. The surroundings must
not only be capable, but must actually accomplish work on the system.
This work results in the ability to reduce the entropy of the
biological system (another way of stating this is that a biological
system is one that does not occur in the most probable state). The
entropy is lowered and this cannot happen without chemical work.
Imagine putting a lid on our pot of boiling water, clamping the lid
down, putting a pressure gauge on the lid, and fitting a pipe from
the lid to a piston arrangement. In the mechanical physics of a
steam engine (which is what we now have), work is defined as w = fd,
where f = force and d = distance. Work can now be accomplished by
steam running through the pipe and pushing the piston. This can in
turn be used to accomplish what we would more popularly conceive of
as work, such as moving a train down the tracks, sawing lumber, or
any number of mechanical tasks.
For reversible processes (where maximum work is possible) DS = qrev / T.
Rearranging the above equation and substituting for q, DS = (DE - wrev) / T. Rearranging
again, wrev = DE - TDS. One might say that the maximum energy
available for work is DE - TDS. For chemical reactions at constant
pressure and temperature, this is stated as Gibb's free energy, which
is the maximum amount of energy "free" to accomplish work (wrev =
wmax = DG). DE is replaced by DH, which is a measure of reaction
energy in terms of heat at constant pressure. Thus the equation, DG
= DH - TDS.
It may be important to note that entropy, like energy,
is measured in joules (actually, J/K). One way to think of entropy
is that amount of energy no longer available for work. The process
of any engine or machine is not 100%. Efficiency is reduced because
not all the energy available is converted to work. The energy flow
through the system must always be greater than the work accomplished,
but in an open system it is possible for work to be done on the
system and decrease the entropy there. This is another way of
stating the second law.
Regards, Paul
Paul D. Brown
Dept of PSES, Ag Sci 242
University of Idaho
Moscow, ID 83844
Phone: 1 (208) 885-7427 or 885-7505
e-mail: pdb@uidaho.edu