A warning: this post starts with thermodynamics, but it will
end with disruptive development. There are many compelling analogs between the
two, but this post will focus on the idea of state and path functions.
From a thermodynamic perspective, a state function is a
property of a system that exist at a moment in time. There are many properties
like this: mass, temperature, etc.
On the other hand, there are properties known as path functions
that represent the transition of the system from over a period of time. These
properties include: heat transfer, work done by or on the system, etc.
Lets highlight the difference with an example: We take two
cups of water both open to the atmosphere (at a pressure of 1 atmosphere). Cup
A starts at 85°C and
Cup B starts at 95°C. We
heat each of the cups up 10 degrees so that Cup A is now at 95°C and Cup B is at 105°C. Up until this point we
have only discussed the state functions associated with the system and, let’s
be frank, it has been pretty boring.
However, if you are familiar with the Celsius scale you will
realize that the water in Cup B at a temperature of 105°C has completely boiled away and
is now steam. It turns out when we look at the heat transfer path function, we
put roughly 50 times more energy into Cup B than Cup A to accomplish what
appeared at first to be the same state function process. What an interesting,
if not totally unforeseen, outcome.
The reason we may have been caught off-guard in the previous
example is that we did not anticipate the path function of water. In
thermodynamics we inherently are drawn to state functions and feel more
comfortable using them. As a fairly firm rule, we try to force path functions
to act like state functions whenever possible, and we (me especially) are
chronically hampered when developing new thermal systems by our dependence on
them.
