I remember when I first learned about
the laws of thermodynamics and the the second one always confused me because it
was about entropy: "the entropy of a closed system can only increase" where
the entropy is the messiness or disorder of a system and I thought, "How in the
world did anyone come up with an equation for messiness? And why in the
world would anyone come up with an equation for messiness? And how did
scientists start to believe as the singer David Burns said from the talking
heads: To answer these questions we have to turn to a German scientist named
Rudolf Clausius who had this amazing ability to make almost every scientist
around him think he was wrong for decades before they finally realized
he's fundamentally correct! Ready for the story? Let's go! I'd like to start in
1849 when Rudolf Clausius was a 27 year old high school teacher. 1849 was when
Clausius read a paper about the theories of a long deceased French scientist
named Sadi Carnot. Clausius decided that some of Carnot's ideas were correct but
he disagreed with the idea that heat is always conserved. In 1850 Clausius
published his theory (that we currently believe is true) that heat can be converted
into work and work into heat. Clausius wasn't the first to promote the idea of
heat work equivalent but he was the first to say that it did not require one
to "cast the theory of Carnot overboard" but "merely the idea that no heat is lost"
In addition Clausius added a new term which was a combination of what he
called the interior work and the interior heat that we now call the
internal energy. With this term Clausius became the first person to
publish a complete version of the first law of thermodynamics!
Although he didn't use the word energy for further 13 years as the term energy
was just becoming popular in the 1850s and 60s, an equation that Clausius
created is still used to describe the first law with the same letters and sign
conventions today! Clausius's publication made his name in science and
soon he earned a job as a professor but it also earned him some enemies. In
Scotland William Thompson whose paper initially sparked Clausius's interest
thought the Clausius was just reiterating the work of a disheveled
Scottish scientist named William Rankine and advised Rankin to send a letter to
the editor to that effect in Germany. A scientist named Hermann Helmholtz had
just written a paper on the conservation of energy and felt that Clausius was
just copying him! In addition all three men decided that whatever Clausius had
not plagiarized was just dead wrong and for many many years
Clausius could not publish anything without letters from Thompson, Rankine, or
Helmholtz or more complaining about it! I tend to side with Clausius on this one. In fact, as far as I can tell Clausius's paper of 1850 is startling in its
accuracy and its importance. I'm not alone in this assessment in 1980 a
historian wrote the following "there is no doubt that Clausius with this paper
of 1850 created classical thermodynamics all preceding except Carnot's is of
small moment." Also, all three men eventually ended up agreeing with
Clausius although they always kept some disdain for the originality of his
arguments or the strength of his positions. Years later Thompson wrote
"the memoir of Clausius contains the most satisfactory and nearly
complete working out of the theory of motive of power of heat but his hypothesis
is so mixed that the general effect is lost." It probably didn't help the
Thompson and Helmholtz specifically were both known for their charm and
charisma and Claudius's personality has been
he lost a time aside from his brother saying he was a man of rare modesty his
son writing that the most principled trait in my father's character was
without doubt the splendid truthfulness of his nature and a letter from a
student years later that described Clausius as "that old grouch"
Eventually both Helmholtz and Thompson were knighted (Helmholtz became Hermann
von Helmholtz and Thompson became Lord Kelvin (like the temperature scale that is
named after him) Despite the attacks Clausius continued to publish his theories
on heat. In 1854 Clausius published his fourth paper on heat and this is the
one where he created entropy, well sort of In this paper Clausius said that they're already two rules. The first one is the
one that heat can be converted into work and work into heat. The second one was
Carnot's theorem that heat engines only work because the heat flows from the hot
source to the cold sink and the amount of heat you get is dependent on the
temperature of both sources. Clausius felt, however, that Carnot theorem in
this form is incomplete because, "We cannot recognize therein with sufficient
clearness the real nature of the theorem and its connection with the first
fundamental theorem" What to do? Clausius knew that Carnot had made this
hypothetical cycle where if you did it one way heat would create work and if
you did it the other way work would create heat this is currently called the
Carnot cycle. Clausius decided that there must be some
mathematical way to make the heat transformations equivalent so if you did
them in the opposite order they would work in the opposite way. He also
determined that this equivalence function had to be a function of the
heat and the temperature. He also noted that less heat at lower temperatures was
equivalent to more heat at higher temperatures so the temperature must be
in the denominator. He therefore decided as a function he was working with Q over
T where Q is the heat and T is most likely "simply the absolute temperature" Clausius also defined the equivalence value of
heat going from temperature 1 to temperature 2 as Q divided by (t2 minus
t1) and gave the letter N for the sum of equivalence values which he
generalized as the integral of the element of heat over temperature. Note
from the present, this function, the heat over the absolute temperature is an
equation for entropy! Although Clausius didn't call it entropy.
Then Clausius decided that if a process was reversible then the sum of these
functions must add to zero. Here is his logic: he said imagine it wasn't true and
the equivalence value was negative if that was the case then the value of the
heat over t2 minus t1 would also have to be less than zero for some
part of it which means that heat would have to flow from the lower temperature
to the higher temperature which is not possible due to Carnot's theory. He then
added if the sum was positive then you do the process in reverse and then the
sum becomes negative and once again you get heat flowing from low temperatures
to high temperatures which is a no-no! Ergo, no matter how complicated a cycle
is if it is reversible then the equivalent values must add to zero
Clausius added that if a process was irreversible meaning you couldn't do it
backwards you couldn't get a negative equivalence value for the same reason
but you could get a positive one. He therefore concluded with his second law
of thermodynamics: By the way I was taught heat can't
flow by itself from a cold object to a hot object because it violates the
second law of thermodynamics but in studying Clausius
I found the reverse to be true meaning Clausius based his ideas of entropy
(or what he called at the time equivalent values) on the principle that heat cannot
flow from a cold object to warmer object by itself and he got that idea from
Sadi Carnot! Fast forward eight years to 1862
that's when Clausius wrote a paper about the equivalence values
(cough-cough entropy) for a system that didn't go in a full circle but started
at one temperature state and ended up at another temperature state. Clausius
decided that heat usually increases the mean distance between molecules which he
called the disgregation (if you've never heard this term it's because we no longer use it)
Clausius also noted that water is strange and that when ice melts the
molecules actually get closer together instead of further apart so he added
that in that case the disgregation is not accompanied by an increase of the mean
distances of the molecules. therefore Clausius uses disgregation had to
do with either the separation of the molecules or their orderliness. Clausius
became the first to state that the one could determine the entropy from the
arrangement of molecules inside a body even if you don't know how much heat was
absorbed. Also when Clausius looked at a single transformation he realized that
a general property of transformations is In other words, entropy of a closed system can
only increase! And that's not all, way back in 1862 some 50 years before Walter Nerst produced it, he came up with the Third law of thermodynamics too writing 3 years later in 1865 Clausius published his ninth paper
on heat in this one he said he was motivated by the desire to " bring
the second fundamental theorem which is much more difficult to understand than
the first to its simplest and at the same time most general form" This paper
is mostly important for the new terminology in it because this is the
paper where he renamed the equivalence value to be the shorter term entropy and
gave it the letter S for no reason I can tell. We still use the letter S for
entropy because of Clausius. Clausius said that he picked the term entropy
from the Greek word for transformation and he "intentionally formed the
word entropy so as to be as similar as possible to the word energy." Clausius
then concluded with his version of the two laws of thermodynamics "the
energy of the universe is constant" and "the entropy of the universe tends to
a maximum" Clausius's version of the two laws of thermodynamics that he wrote
down in 1865 are still considered correct today! Meanwhile William Thompson
one of Clausius's big critics was working on his own version of the second
law of thermodynamics albeit one without an equation years before in 1852.
Thompson wrote that there was always a waste of mechanical energy available to
man when heat is allowed to pass from one body to another at a lower
temperature. By 1862 Thompson declared that the
second great law of thermodynamics "involves a certain principle of
irreversible action in nature it is thus shown that although mechanical energy is
indestructible there is a universal tendency to its dissipation which
produces a gradual augmentation and diffusion of heat cessation of motion
and exhaustion of Potential energy through the material
universe." With entropy Clausius had given the "irreversible action of nature" an
equation and a name! But wait, you say, (or maybe you say) heat over temperature is
not the equation I learned for entropy! That is probably because you and I were
taught Boltzmann's entropy equation. You won't be surprised to learn from its
name the Clausius did not create Boltzmann's entropy equation but you
might be surprised to learn that Boltzmann didn't create it either! Even
though it is carved on his gravestone. So, how did we get from Clausius to
Boltzmann's equation and how did Boltzmann get an equation written after
him and a constant named after him that he didn't directly create? That's next
time on the lightning tamers if you're interested I already have a video about
the first law and I have a video about the third law (I didn't do them in order)
I have a lot of videos you should check them out you should give me a thumbs up
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I really appreciate it but if you're broke you can just give me a thumbs up
and a comment and tell me if I made any darn sense at all. Thanks a lot have a
great day
