Professor Dave again, let's tackle the
second law of thermodynamics.
The first law of thermodynamics told us about the
relationship between internal energy,
heat, and work. The second law will
introduce one of the most confusing
concepts in physics: entropy. Let's go
through this law and examine how the
concept of entropy was derived as a
result. The second law came about through
the work of a fellow named Sadi Carnot
and his study of heat engines. A heat
engine is one that absorbs heat and uses
it to do work, like the steam locomotives
of the 19th century, which absorbed the
heat from a coal furnace to generate
steam which would then move pistons
connected to the trains wheels. Excess
heat from the hot reservoir that is not
actively used to produce work will move
to a cold reservoir, which has a lower
temperature than the hot reservoir.
Carnot understood that the maximum work
or W net that can be done by one cycle
of such an engine is equal to the heat
input or Qh minus the heat output or Qc.
Since any heat lost will not be able to
be converted into work, due to the first
law of thermodynamics, if there was truly
zero heat loss we could say that all of
the heat is transferred to work and the
engine operates at one hundred percent
efficiency. Unfortunately this is not
physically possible for a number of
reasons. First, the only way to achieve
one hundred percent efficiency would be
if every process in the engine were
completely reversible, meaning both the
system and surroundings could return to
their original state. This is known as
Carnot's principle. But any real engine
involves moving parts that produce
friction and sound, so some energy must
always be lost to the surroundings.
This conclusion does not immediately follow
from the first law of thermodynamics so
it was formulated into the second law,
which states that no
cyclic process can convert some quantity
of heat entirely into work, some of this
heat will always be lost to the
surroundings. This is a variation of
another way of expressing the second law
which can also state that heat
spontaneously flows from regions of high
temperature to regions of low
temperature, and not the other way around.
These expressions can be considered two
sides of the same coin, since heat
therefore can't flow spontaneously from
the cold reservoir to the hot reservoir
of a heat engine, further supporting the
idea that heat is always lost to the
environment as the engine runs. But this
is not just a limitation of our
technology, even a purely hypothetical
perfect heat engine called a Carnot
engine, can never operate at one hundred
percent efficiency. This is a
mathematical limitation of heat flow.
Whichever way we choose to look at the
second law it will inevitably result in
the discussion of a peculiar concept
called entropy. Entropy is a term that
represents the inevitable partial loss
of a heat engine's ability to do work.
It is a state function measured in joules
per Kelvin and it will be represented by
the letter S. The change in entropy is
given by heat over the kelvin
temperature for a reversible process and
a mathematical ramification of this
expression is that the change in entropy
is 0 for a Carnot engine. This can be
extended to say that the change in
entropy of the universe will be zero for
any reversible process, where the
universe is understood to mean the
system plus the surroundings. However, no
process is truly reversible, so we should
rather say that the change in entropy of
the universe for any spontaneous process
will be greater than zero, or that for
any spontaneous process the entropy of
the universe is always increasing, which
is another common articulation of the
second law. The implications of this law
are so astounding that they have
philosophical impact. If we take entropy
to mean disorder it
shows that the universe tends to move
towards maximum disorder, and while order
can spontaneously form on the local
level like when water freezes to form
ice or in the case of any living
organism, this will always be accompanied
by a dispersal of energy that increases
the disorder of the universe as a whole.
Entropy can be rationalized if we
examine the concept of microstates,
introduced by Ludwig Boltzmann.
A microstate is simply a specific
configuration of all the particles and
energies in a system. The dispersal of
matter and energy, which is always
accompanied by an increase in entropy,
will tend to be spontaneous. Things move
towards more disorder because of this
equation, where S equals k, the Boltzmann
constant, times the natural log of W,
where W is the number of microstates
possible for a system. This is best
understood with an example. Say there are
four balls to be distributed amongst two
boxes. We could have all four in one,
three and one and one in the other, two
and two, one and three, or all four in
the second box. If these balls are all
different colors, some distributions will
contain a number of different
microstates. Statistical mechanics tells
us that the most probable distribution
will be the one with the most
microstates, as in this case the
probability of finding the system in one
of these microstates with two and two is
6 out of the 16 total possible
microstates. So this is a mathematical
reasoning for why entropy tends to
increase spontaneously in a closed
system, whether this involves the
dispersal of matter through space or the
dispersal of heat energy from hot to
cold objects. Entropy is an extremely
difficult concept to grasp and one could
design an entire course around this
subject alone, so don't worry too much if
this seems confusing. For now, if we can
just grasp a few basics about how the
second law of thermodynamics was derived, we will
be just fine. Let's check comprehension.
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