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 because it's good karma. You should share
it on social media because that's even better karma if you even want better
karma than that you can become a patron and then you have me thank you as I'm
going to do right now: thank you patrons. 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