Dr. Rudolf Clausius: The Laws of Thermodynamics

Part II of our December Thermodynamics Extravaganza! Aarati tells the story of the German scientist who formally stated that 1) energy is conserved and 2) entropy is always increasing.

Transcript

Aarati Asundi (00:12)
Hi everyone and welcome back to the Smart Tea Podcast where we talk about the lives of scientists and innovators who shape the world. I'm Aarati.

Jyoti Asundi (00:21)
I'm her mom, Jyoti.

Aarati Asundi (00:23)
And welcome back everyone to our December extravaganza on thermodynamics.

Jyoti Asundi (00:29)
Yes, we are doing three scientists in a row where the work of one physicist building the work of the next on and so forth until we are doing three in a row.

Aarati Asundi (00:42)
Yeah. So if you didn't listen to the previous episode on Sadi Carnot, I highly recommend you go back and listen to that first and then come back to this episode because today we're going to be talking about another physicist who built on the work that Sadi did. 

Jyoti Asundi (01:00)
Yes, I'm so excited to listen to this. And I remember that Sadi Carnot was in France but then now we are moving over to a scientist in Germany.

Aarati Asundi (01:12)
Yes.

Jyoti Asundi (01:13)
And how many years later is this work?

Aarati Asundi (01:15)
Only a few years, only a couple of years later. 

Jyoti Asundi (01:18)
Oh that's pretty good. Okay.

Aarati Asundi (01:20)
Yeah, like maybe... I think Sadi Carnot died in 1832, I think, if I remember, and then his work was translated two years later. And then very shortly after that, it made its way into the hands of the scientist today.

Jyoti Asundi (01:35)
Perfect.

Aarati Asundi (01:36)
So we did mention in the end of the last episode, and of course, if you've looked at the title of this episode already, you know that we're going to be talking about Rudolf Clausius, who is credited with laying down the first two laws of thermodynamics.

Jyoti Asundi (01:52)
Wow! So we started with Sadi Carnot, the father of thermodynamics and then now we are doing Rudolf Clausius who laid down the first two laws of thermodynamics. That is pretty awesome stuff we are doing here. This is fun!

Aarati Asundi (02:07)
Yeah. Sadi Carnot kind of laid down the basic fundamentals of thinking about how heat and work are kind of related to each other. And now, Rudolf Clausius comes in and really defines a lot of these laws and how things are working. So he has done a lot. This episode is going to be very physics heavy, so prepare yourself. 

Jyoti Asundi (02:31)
Whoo okay okay.

Aarati Asundi (02:32)
Yes. But before we get into that, first a little bit about his life and how he got into thermodynamics to begin with. So Rudolf Julius Emanuel Clausius...

Jyoti Asundi (02:44)
Whew! What a mouthful!

Aarati Asundi (02:46)
Yeah. Was born on January 2nd, 1822 in Koslin Poland in the province of Pomerania, Prussia. He was the youngest of... get ready...18 children.

Jyoti Asundi (03:03)
Wow from the same mom?!

Aarati Asundi (03:05)
Don't know about the same mom, but that's a good question. 

Jyoti Asundi (03:10)
Oh yes, yes.

Aarati Asundi (03:10)
If so, that poor lady.

Jyoti Asundi (03:13)
Oh my goodness. She spent most of her child bearing then and child rearing of course.

Aarati Asundi (03:20)
Yeah. His father, because of course, during these times, we know more about the father than we do about the mother always. That's kind of how goes. His father was a Protestant pastor and had founded a small school where he served as principal.

Jyoti Asundi (03:38)
Okay.

Aarati Asundi (03:39)
So Rudolph was educated early on in this school. In 1838, when he was about 16, he continued his education at the Stetten Gymnasium. And gymnasium is the word that they were using for high school.

Jyoti Asundi (03:54)
Oh interesting. 

Aarati Asundi (03:55)
Yeah.

Jyoti Asundi (03:56)
I wonder if schools used to be more sports heavy in those days. Maybe that's why they were called gymnasium. It was more focused on physical development. 

Aarati Asundi (04:05)
I don't know. I don't know. When I was reading his story, maybe it's a German specific thing. I don't know. Somebody in the audience let us know. But when I was reading his story specifically, there was a lot of gymnasiums involved. It seemed like it was another word for high school. And I think I looked it up also and it said it was an antiquated term for high school.

Jyoti Asundi (04:26)
For high school. Hmm.

Aarati Asundi (04:27)
Yeah. I don't know. Maybe it just, it was the word and then it fell out of favor or it was a, it's a German thing. Not a hundred percent sure, but.

Jyoti Asundi (04:36)
Okay.

Aarati Asundi (04:37)
So he goes to high school and then two years later in 1840 he enrolled in the University of Berlin. He was initially a bit torn as to what he wanted to study. He was initially drawn to history but ultimately wound up completing a degree in math and physics. He graduated in four years, and then he spent one year teaching advanced math and physics at the Frederick Werder Gymnasium. So again, there's that gymnasium. Yeah.

Jyoti Asundi (05:00)
Okay, once again, gymnasium and it's probably high school, so now he's a high school teacher.

Aarati Asundi (05:06)
Mm-hmm. So he then went on to the University of Helle to study for his PhD in physics. 

Jyoti Asundi (05:12)
Okay. 

Aarati Asundi (05:13)
Here his dissertation aimed to explain, among other things, why the sky was blue and why we see different colors at sunrise and sunset.

Jyoti Asundi (05:24)
Oh! The fractionation of light.

Aarati Asundi (05:26)
Yes. So in his dissertation, he proposed that it was because of the refraction and reflection of light, which ultimately turned out to be incorrect. Now we know it's due to the scattering of light. So when a light wave hits a particle of something in the air, it's deflected in a bunch of different directions. 

Jyoti Asundi (05:51)
Yes. It splinters into its component waves

Aarati Asundi (05:54)
Yeah. So He turned out to be incorrect about that. But the math that he used in his dissertation was novel and pushed the boundaries of mathematics. And so it was still very impressive. After graduating, he returned to the Frederick Werder Gymnasium and continued to teach there for the next six years.

Jyoti Asundi (06:14)
Wow! Must have liked it.

Aarati Asundi (06:16)
I think so. I was also thinking about how these high school students had PhD level math and physics people teaching them. 

Jyoti Asundi (06:29)
Yes.

Aarati Asundi (06:29)
I feel like that's amazing. And I think it was very common for the time. I've heard this in other stories. I think Santiago Ramon y Cajal was also like that, where people who had PhDs in biology went and taught high schoolers.

Jyoti Asundi (06:45)
Yes, put the education of the young minds into competent hands.

Aarati Asundi (06:50)
Yes, exactly.

Jyoti Asundi (06:51)
And it was obviously a noble profession. It's still a noble profession, but it's enough by society these days in terms of payment and all that, which is very sad actually.

Aarati Asundi (07:04)
Yeah, and I don't want to get too political, but I saw recently that there was like a proposal or something for certain college degrees to like devalued basically. So like if you got a PhD in education a degree in nursing or a degree in physical therapy or something, it would no longer be called a doctorate. It would no longer have that same status.

Jyoti Asundi (07:27)
Oh no. Oh that is so sad.

Aarati Asundi (07:28)
Yeah. And people were pointing out that a lot of these degrees are actually degrees that are pursued by women. And so it was just another way to devalue like teaching, nursing, all of these kind of professions. 

Jyoti Asundi (07:40)
Oh no, this is so sad. We are really going backwards in a very big way.

Aarati Asundi (07:46)
I know. It's ridiculous and you know, we know people like that. We know people who have degrees in physical therapy and in...

Jyoti Asundi (07:54)
Absolutely

Aarati Asundi (07:54)
You know, nursing and stuff. And that's hard work. Like, that's... my God, I couldn't do it.

Jyoti Asundi (07:57)
Yes, yes, they have killed themselves and got into deep student loans for getting these degrees and and now it's like devalued, which obviously means that now their pay will be comparatively lower. That is a very sad.

Aarati Asundi (08:11)
Yeah. And even education, like the amount of work these teachers put in to making classes educational and fun and engaging is just incredible. 

Jyoti Asundi (08:22)
Yes, absolutely.

Aarati Asundi (08:23)
And you cannot devalue that.

Jyoti Asundi (08:26)
You cannot devalue that. pay for this as a society down the line because basically you're not investing in the growth of young minds. So we are going to see a lack of analytical thinking. And so then young people then will tend to kind of follow the drum. They'll find somebody who they believe in and just go by what one person says, sort of like a cult mentality. If so and so says it, then I'm going to believe it and move on from there. 

Aarati Asundi (08:58)
Yeah, the critical thinking is lost.

Jyoti Asundi (09:00)
Correct. Very sad, actually.

Aarati Asundi (09:03)
And education also just exposes you to so many different facets of the world, so many different types of people. So there's that that's being lost as well. So...

Jyoti Asundi (09:12)
Yes, very sad. And then you become insular when you understand other cultures, when you don't understand what's happening with other people in other parts of the world. You become extremely insular, you become more judgmental, you become less tolerant. ⁓ So it's a shame and it's a big loss for society.

Aarati Asundi (09:33)
Yeah. So let's go back to happier times in the 1800s.

Jyoti Asundi (09:37)
Yes, where Clausius with his PhD degree is teaching young high schoolers about math and physics and all that good stuff.

Aarati Asundi (09:46)
Yes. And then on the side, he continues to study physics and math himself.

Jyoti Asundi (09:52)
Keeping abreast of what's going on in that field.

Aarati Asundi (09:56)
Mm-hmm. In 1849, he comes across a paper written by his contemporary, William Thompson, who we've talked about before, AKA Lord Kelvin...

Jyoti Asundi (10:09)
That's right.

Aarati Asundi (10:10)
...about the theories of heat. And in this paper, William Thompson referenced Sadi Carnot's work on how heat can be turned into work and vice versa. 

Jyoti Asundi (10:20)
Okay.

Aarati Asundi (10:21)
So Rudolph gets interested in this. He starts digging deeper into Sadi Carnot's work. And he determined that Sadi had some very good points. But there was one glaring problem. And we did talk about this a little bit last episode. The problem is that Sadi wasn't sure exactly what heat was.

Jyoti Asundi (10:42)
Yes, okay.

Aarati Asundi (10:44)
So there were two hypotheses at the time. Sadi Carnot, Emile Clapeyron, who is the guy who translated Sadi's work from French into English.

Jyoti Asundi (10:53)
Yes. Mm-hmm.

Aarati Asundi (10:55)
So he, Sadi, and a majority of other physicists actually believed that heat consisted of an invisible weightless fluid called caloric. And that flowed from hotter objects to colder ones, the same way that water flows from higher levels to lower levels. Because of this, Sadi believed that no heat or in other words, none of this caloric substance was lost in his theoretical engine. Instead, he thought that heat was this substance that was doing the work as it flowed through the system.

Jyoti Asundi (11:33)
Yes, got it. Okay.

Aarati Asundi (11:36)
But Rudolf took particular issue with this statement that no heat is lost. He fell into a smaller camp of physicists who believed that heat was the transfer of kinetic energy of particles in one substance to another.

Jyoti Asundi (11:55)
Yes, getting closer to the truth.

Aarati Asundi (11:57)
Mm-hmm. And because of this, he believed that in Sadi's machine, and quote, "In all cases where work is produced by heat, a quantity of heat proportional to the work being done is consumed. And inversely, by the expenditure of a like quantity of work, the same amount of heat may be produced, end quote.

Jyoti Asundi (12:20)
Okay, so basically it's a back and forth, a reversible situation. Heat can become work and work can become heat. 

Aarati Asundi (12:28)
Yes.

Jyoti Asundi (12:28)
In an equivalent way, sort of.

Aarati Asundi (12:30)
Yes. And so he is the one who's really introducing this idea of transformation, that heat is not a fluid that is doing the work, but rather it's transforming into the work.

Jyoti Asundi (12:43)
Yeah. So heat itself becomes work, work itself becomes heat. Yeah.

Aarati Asundi (12:48)
Yes. And so they're like two sides of the same coin kind of thing.

Jyoti Asundi (12:51)
Yeah. It's like it's a water and ice basically. Water becomes ice, ice can become water, that kind of thing. So same thing, heat can become work, work can become heat. It's not like there is a substance there that is now flowing and doing something and creating work like that. They are not two separate entities.

Aarati Asundi (13:09)
Yes, and that's why he took issue with Sadi Carnot saying that no heat is lost. He was like, yeah, heat is lost because it's being transformed into work. 

Jyoti Asundi (13:15)
Yes. Yes, it's become work now. Yes. 

Aarati Asundi (13:19)
Yeah, so you did lose heat.

Jyoti Asundi (13:21)
Yeah, the piston moving was work and that much heat is lost.

Aarati Asundi (13:25)
Yes. But it's important to note that Rudolph wasn't the first ever physicist to say this. And in fact, he relied heavily on experiments of an English physicist, James Prescott Joule who proved experimentally that heat was in fact a form of energy and not an invisible fluid. And of course, joule is the unit of energy that we now know and use in physics.

Jyoti Asundi (13:48)
That's right. That's right. Those are these are these are like the classic names that are we are using even today. Ampere, Joule, Kelvin, all these are the units of major things like work and heat and all of that. 

Aarati Asundi (14:04)
Yeah, and they're all running around this thermodynamics problem at the same time. Yeah.

Jyoti Asundi (14:09)
At the same time. Yeah. Tackling it all. It's a nice thing to think about where they are all sharing their knowledge with each other equally so that they all get to the right solution and to the right conclusions faster. Serving mankind that way rather than saying this is my idea and I'm going to horde it and I'm not going to share. It's very cute to see that.

Aarati Asundi (14:31)
Yeah, no, they would absolutely, they publish it, then everybody would look at it, poke holes in it, they refine it, know, so huge amount of work happening right now.

Jyoti Asundi (14:38)
Yes, yes. And that's how we have the thermodynamics as it stands today, thanks to all these people and their total focus on understanding the subject rather than self-glory.

Aarati Asundi (14:51)
But the other actually interesting tidbit I found was that Sadi Carnot actually later in his life came around to the same conclusion that heat was kinetic energy between molecules and it wasn't an invisible fluid, but he died before these thoughts could be formally published.

Jyoti Asundi (15:13)
Or maybe they got destroyed by that stupid cholera that he got. 

Aarati Asundi (15:18)
I think a lot of it did, but some there were some private notes that somehow survived and those private notes were only made public in 1890, which is years after all of this is taking place. Rudolf Clausius Joule's experiments and everything is happening like 50 years earlier. And then in 1890, 50 years later, people are like, "Oh! Sadi Carnot actually also came around to the same conclusion at some point."

Jyoti Asundi (15:47)
Yeah, yeah. That one piece of paper that survived that destruction of all his effects shows that he was on the right track at the end.

Aarati Asundi (15:58)
Yeah, somebody found it tucked away. His brother's son or something must have opened a book and said, hey, Uncle Sadi had this. Yeah.

Jyoti Asundi (16:06)
Here he says that already.

Aarati Asundi (16:09)
Ok, so back to Rudolph. So in 1850, Rudolph published a paper called On the Motive Power of Heat, which is largely credited with being the first complete version of the first law ever written.

Jyoti Asundi (16:22)
Mm-hmm. Wow.

Aarati Asundi (16:24)
In this law, he introduced some new terminology, interior work and interior heat, which today we basically just internal energy. 

Jyoti Asundi (16:36)
Okay.

Aarati Asundi (16:37)
And he gave this the symbol U. The equation that he wrote down in his paper was delta U equals Q, which stands for heat, minus W, which stands for work. So in other words, the change in the internal energy is equal to the amount of heat you put into the system minus the amount of work that you get out.

Jyoti Asundi (17:01)
Yes, okay.

Aarati Asundi (17:03)
This was a breakthrough in physics research and skyrocketed Rudolph's career. Because of it, he was offered an academic position at the Royal Artillery and Engineering School in Berlin and became a docent at the University of Berlin. 

Jyoti Asundi (17:17)
Oh nice.

Aarati Asundi (17:19)
However, I was also watching a video on YouTube from the channel Kathy Loves Physics. She's great, by the way. If anyone is interested in anything related to physics and history of physics especially, go check her out. She really lays it down a lot of interesting tidbits. And she really knows what she's talking about when she's talking about all these equations and things like that.
But one thing I picked up from her channel was she was saying that Rudolph's ideas about the relationship between heat and work were very similar to and definitely inspired by many of his including William Thompson, William Rankine, and Herman Helmholtz. And they read Rudolph Clausius's papers on the first law of thermodynamics... 

Jyoti Asundi (18:08)
Yeah.

Aarati Asundi (18:09)
...they essentially were like, he's copying us. This is our work, you know, and he's just rephrasing it or, you know, relying heavily on our work to draw the same conclusions that we are drawing.

Jyoti Asundi (18:23)
So basically, Rudolf presented the same ideas in a very refined and concise way so that it could kind of be put into an equation rather than just talking about it and trying to theorize about it. He came up with an equation that explained it.

Aarati Asundi (18:41)
Yeah, so that's what we give him credit for today. It's like a lot of people were circling the point here with like William Thompson, William Rankine, you know, all these people, they're doing experiments that are kind of leading to the same conclusion. And Rudolph Clausius is taking all of this and he's like, here it is. Here's the rule in a very succinct mathematical way...

Jyoti Asundi (19:04)
Yes.

Aarati Asundi (19:04)
...that is supported by all of your information,

Jyoti Asundi (19:07)
That's right.

Aarati Asundi (19:07)
...all of your experiments on heat, your experiments on energy, your experiments on work. All of this is supporting this one universal truth. Here's the truth. That's the first law of thermodynamics. 

Jyoti Asundi (19:20)
Got it okay.

Aarati Asundi (19:20)
And everyone's like, yeah, that's basically what we're saying. And he's like, yeah, but I said it. 

Jyoti Asundi (19:25)
That's what I said. Isn't that what I just said?

Aarati Asundi (19:27)
Yeah. And he's like, no, I said it. Yeah. Yeah.

Jyoti Asundi (19:31)
Yeah. I can see that. Okay.

Aarati Asundi (19:34)
Yeah. So because of this, because they kind of were like, you're copying us, whenever Clausius tried to publish a paper over the next few years, they would hound the editors of the journals to complain about how Clausius had copied them or gotten things wrong.

Jyoti Asundi (19:49)
Hmm.

Aarati Asundi (19:51)
But as we were just saying, one science historian wrote, "There is no doubt that Clausius with his paper created classical thermodynamics. All proceeding except Carnot's is of small moment."

Jyoti Asundi (20:05)
Oh wow, okay, okay.

Aarati Asundi (20:08)
Yeah. So it's like everyone else is supporting main... thought.

Jyoti Asundi (20:13)
Thought. He is able to bring all these multiple thought streams of multiple people together to create one very clean equation that becomes the first law of thermodynamics.

Aarati Asundi (20:25)
Yes. So Rudolf continues to shine and continues to publish papers on heat. He also continues to look at Carnot's cycle and his next conundrum that he was like, something's up here...

Jyoti Asundi (20:40)
Yeah, something is not quite right kind of thing, yeah.

Aarati Asundi (20:43)
Yeah. Was that he knew Carnot's cycle consisted of reversible steps where you could do the four steps in one way and get heat or do them reverse and get work.

Jyoti Asundi (20:53)
Yeah remember one and three is the inverse of step one. Step four is the inverse of step two in Carnot's cycle.

Aarati Asundi (21:03)
Yeah. So he was like, yeah, great. Perfect. But he also believed that heat always flowed from the hotter object to the colder one and never reverse. So mathematically, if you're only working with heat, this reversibility doesn't make sense unless heat can flow from a cold object to a hot object.

Jyoti Asundi (21:25)
To the hot. Yeah, yeah correct.

Aarati Asundi (21:27)
Yeah, which even Carnot knew it didn't do. So...

Jyoti Asundi (21:30)
That's right.

Aarati Asundi (21:31)
He's like, know, mathematically, if you're only looking at math, like if you're looking at the physics, it makes sense. But if you're looking at just mathematically, how do you reconcile this with numbers? It doesn't make sense unless you can have heat flowing from cold objects to hot objects, which we know it doesn't do so how do you...

Jyoti Asundi (21:53)
It doesn't do. Yes.

Aarati Asundi (21:54)
Yeah, so how do you define this mathematically in a way that makes sense? 

Jyoti Asundi (21:57)
How do you reconcile it? Yes.

Aarati Asundi (21:59)
Yeah, how do you reconcile the physics with the math?

Jyoti Asundi (22:02)
Correct.

Aarati Asundi (22:03)
So in 1954, Rudolph published his fourth paper on heat in which he laid out a term called the equivalence value, which was equal to heat divided by temperature. So now if temperature is held constant, if heat goes in, you get a positive value. And if you reverse it, when heat comes out, you get a negative value.

Jyoti Asundi (22:27)
Yeah. Yeah. Yeah, Okay.

Aarati Asundi (22:30)
So let's for example, just 100 in, 100 out. So when you add these two values together, you do 100 heats in plus negative 100 to take the heat out.

Jyoti Asundi (22:45)
Take the heat out. Yeah.

Aarati Asundi (22:46)
Yeah, you get a net equivalence value of zero.

Jyoti Asundi (22:50)
Correct. Correct.

Aarati Asundi (22:51)
So in this case, the system is perfectly reversible. That's Carnot cycle. There's no heat loss due to friction or leaks or anything like that. 

Jyoti Asundi (23:01)
Correct.

Aarati Asundi (23:02)
But remember, again, Sadi's engine was an ideal.

Jyoti Asundi (23:06)
Yes, and it was only theoretical. Yes.

Aarati Asundi (23:08)
Yes. So in real life, most systems are not perfectly reversible.

Jyoti Asundi (23:14)
Yes.

Aarati Asundi (23:15)
So if you imagine you put heat into the system, let's say 100 again, now the system loses energy due to heat leaking or friction. So when you reverse the system, you get out less heat than you put in. So let's say you get back only 80 % because the other 20 % was lost.

Jyoti Asundi (23:34)
Yeah, you dissipated it somehow. Yeah, wastage. 

Aarati Asundi (23:38)
Yeah. So now you have 100 heat in plus negative 80 heat out, which gives you a net equivalence value of 20.

Jyoti Asundi (23:49)
Yes.

Aarati Asundi (23:50)
And this is a bigger number than 0, obviously. But could you ever get a net equivalence value that was less than 0? So could you ever put in 100 % heat and get back out 120%? 

Jyoti Asundi (24:05)
120 yes

Aarati Asundi (24:08)
Yeah. So Rudolph was thinking about this, and he was like, the only way for that to ever happen, if the system is a closed system and you're not putting in more heat somehow, to get that 20 % extra back out,

Jyoti Asundi (24:24)
That's right.

Aarati Asundi (24:24)
Yeah, so it's a closed system. The only way to do that would be if somewhere in the system, the heat was flowing from a lower temperature to a higher one, which we know is impossible. In a natural system, that doesn't happen.

Jyoti Asundi (24:37)
Okay.

Aarati Asundi (24:38)
So Rudolph stated that in a complete cycle, if it's reversible, you will always get an equivalence value that is greater or equal to zero. You can never get a negative equivalence value. 

Jyoti Asundi (24:49)
You can't get a negative. Yeah, because heat doesn't flow the opposite direction. It doesn't go from cold to hot.

Aarati Asundi (24:56)
So this was another big breakthrough. In 1855, he was appointed to the chair of mathematical physics at the Polytechnikum in Zurich and appointed as a professor at the University of Zurich. So he's really- his work is really capturing the attention a huge audience.

Jyoti Asundi (25:15)
Yeah, he's making waves there.

Aarati Asundi (25:18)
And at the University of Zurich, he's able to reach an even wider audience of physicists and push forward his ideas because the University of Zurich was and probably still is known for...

Jyoti Asundi (25:31)
Well known. Yeah, it's a better platform. It's a more widely regarded platform. And so he has a bigger megaphone basically now to push his ideas out.

Aarati Asundi (25:43)
Yes. Around this time, he also got married to a woman named Adelheid Rimpam. And together they started a family.

Jyoti Asundi (25:53)
Mm-hmm.

Aarati Asundi (25:54)
So things are going pretty well.

Jyoti Asundi (25:56)
Pretty well for him, yeah.

__________________________________________________________________________________________________________________

Aarati Asundi (26:04)
Hi everyone, Aarati here. I hope you're enjoying the podcast. If so, and you wish someone would tell your science story, I founded a science communications company called Sykom, that's S-Y-K-O-M, that can help. Sykom blends creativity with scientific accuracy to create all types of science, communications, content, including explainer videos, slide presentations, science, writing, and more. We work with academic researchers, tech companies, nonprofits, or really any scientists. To help simplify your science, check us out at sykommer.com. That's S-Y-K-O-M-M-E-R.com. Back to the story.
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Aarati Asundi (26:50)
So then eight years later in 1862, Rudolph published another paper on his equivalence values that asked the question, now what if the system's not reversible? What if it just went in one direction and stopped? 

Jyoti Asundi (26:05)
Yes.

Aarati Asundi (26:06)
So if you're putting in heat and you're not reversing the system to get the heat back out, then the heat just stays in the system and increases the temperature until the object reaches a new internal state.

Jyoti Asundi (27:20)
That's right. Okay

Aarati Asundi (27:21)
So what is changing then? What's happening to the molecules in that system as it heats up?

Jyoti Asundi (27:27)
Yes, yes. Correct, correct.

Aarati Asundi (27:31)
So at first, when Rudolph looked at only gases, he thought when you increase the temperature of a gas, it expands, right? We have PV equals nRT. So pressure stays constant. Then volume increases when temperature increases. 

Jyoti Asundi (27:46)
Correct.

Aarati Asundi (27:47)
And so that must mean that the gas molecules must be getting further apart from each other for volume to be increasing. 

Jyoti Asundi (27:55)
Yes.

Aarati Asundi (27:57)
But then he realized that doesn't work for everything. So for example, some substances like water, if you have liquid water, and then it becomes solid ice, when the molecules freeze in this very structured lattice shape, they're kind of far away. But when the temperature increases, and the ice melts, the water molecules actually get closer together.

Jyoti Asundi (28:23)
That's right, that's right because they are not bound in a very defined lattice structure. 

Aarati Asundi (28:28)
Yes.

Jyoti Asundi (28:28)
So they are now free flowing, they can use less space to sit in a little bowl. Yeah, yeah, got it.

Aarati Asundi (28:34)
Yeah. And then if you heat it up even more into steam, then the molecules get further apart.

Jyoti Asundi (28:41)
Correct. It can go back and forth basically. Yeah, when it's cold, it's using more space. Then it becomes liquid, it uses less space. Now it's become gas, which means even more heat than liquid, and now it is using more space. So the coldest is using more space, and the hottest is using more space. The intermediate where it's water and it's in between the coldest and the hottest is using less space than either of those.

Aarati Asundi (29:07)
Yes, exactly. And so it's like, I can't write one just universal law that says, when you increase temperature, the molecules are going to get further apart, or volume is going to increase. That's not true. So instead, he concluded that when the temperature in the system increased, the molecules became more disorderly.

Jyoti Asundi (29:31)
Yeah, He's coming up with the right points now. Yes.

Aarati Asundi (29:36)
Mm-hmm. So in the real world, when we have equivalence values that are always positive, that means that molecules are always getting more disorderly.

Jyoti Asundi (29:48)
Yes. Are we headed towards entropy?

Aarati Asundi (29:51)
Yes, we are. 

Jyoti Asundi (29:53)
Ooooh yes!

Aarati Asundi (29:54)
Yes, we are. We're getting there. So in ideal cases, you can have an equivalence value of 0, which means the molecule's orderliness stays the same... 

Jyoti Asundi (30:05)
Yes.

Aarati Asundi (30:06)
...but you can never have a closed system where the orderliness of molecules actually increases because you can never have an equivalence value that is less than 0.

Jyoti Asundi (30:18)
Yeah, yeah, yeah.

Aarati Asundi (30:20)
So Rudolph spends the next couple of years refining his theories, and three years later, in 1865, he publishes "On Different Forms of the Fundamental Equations of the Mechanical Theory of Heat" which officially renames the equivalence value into entropy.

Jyoti Asundi (30:40)
Ah! Yes, that initial thought that he had, there's an equivalence value when he said that he's really thinking about the heat going in causing agitation in the molecules. It's when I think of entropy, I always think of a three year having a sugar high. 

Aarati Asundi (31:02)
Just going crazy.

Jyoti Asundi (31:03)
Yeah, because you can give a system a lot of heat. And the molecules inside start to be agitated and bounce off the walls. And for me when I want to visualize entropy, I always think of young little kids getting a lot of sugar

Aarati Asundi (31:20)
Yeah, you give them a lot of energy and now they're going crazy. Yeah.

Jyoti Asundi (31:23)
Yeah, and now they're bouncing, yeah. Yeah, it's really that for me that's a very visual representation of entropy. That's what entropy is all about. 

Aarati Asundi (31:31)
Yes, that's exactly what it is.

Jyoti Asundi (31:32)
You give them heat instead of heat, you give them sugar. That's it. Yeah.

Aarati Asundi (31:36)
Yep. Good one. Yeah, so he, his equivalence value is basically entropy. He renames it entropy. gives it the letter S for some reason. No one knows why.

Jyoti Asundi (31:51)
Hmm.

Aarati Asundi (31:52)
But the word entropy comes from the Greek word for transformation. And it is a word that Rudolph intentionally chose because it was similar to the word energy. So he wanted people to link those two things.

Jyoti Asundi (32:07)
Yes, he wanted it to be linked. Yeah. He seems like a really smart guy. Yeah.

Aarati Asundi (32:13)
Yes, he's a smart-tea. 

Jyoti Asundi (32:16)
⁓ One more smarty. Good one. I like that.

Aarati Asundi (32:18)
One more smarty. Yes. 
This paper also officially lays out the first two laws of thermodynamics in a way that we recognize them today. The first law that he wrote is that, "The energy of the universe is constant." And so other ways that we've said that is like energy can neither be created nor destroyed. And so that's, again, getting into that heat is transforming into work and vice versa. It's not being destroyed. It's not being created.

Jyoti Asundi (32:53)
Yeah, and you're not creating something new there. It's just heat becoming energy, energy becoming heat. 

Aarati Asundi (32:58)
Yes.

Jyoti Asundi (32:59)
You're not, you're not, you know, creating something different entirely.

Aarati Asundi (33:05)
Exactly. And the second law that he wrote was the entropy of the universe tends to a maximum. In other words, entropy is always increasing.

Jyoti Asundi (33:15)
Always, yeah, it's always the universe is going towards disorder. 

Aarati Asundi (33:19)
Yes.

Jyoti Asundi (33:20)
Which we see even amongst people and societies. We are all headed towards more and more disorder. 

Aarati Asundi (33:27)
Yeah, we're all going crazy here.

Jyoti Asundi (33:29)
It's built into us, can't do anything about it.

Aarati Asundi (33:35)
Yeah, might as well just go along for the ride. Yeah.

Jyoti Asundi (33:37)
Might as well just go along with this disorder.

Aarati Asundi (33:41)
Meanwhile, although he's thriving in Zurich, he starts to miss Germany.

Jyoti Asundi (33:48)
Aw!

Aarati Asundi (33:49)
Over the years, he had actually turned down offers from German universities like the Polytechnic University in Karlsruhe and the Polytechnic in Brunswick, because neither of them really offered the same scientific excellence and opportunities, or the ability to reach such a wide audience.

Jyoti Asundi (34:06)
That he was able to find in Zurich. Okay.

Aarati Asundi (34:08)
Yes. But by 1867, when the University of Würzburg offered him a professorship, he finally couldn't resist anymore. He deeply regretted leaving Zurich, but he was very happy to be going back to Germany at last.

Jyoti Asundi (34:23)
Yeah, yeah, he's doing his best work in every place. So, yeah.

Aarati Asundi (34:29)
Mm-hmm. This same year that he moved from Zurich back to Germany in 1867, Rudolf Clausius wrote another paper on examining how temperature related to molecular movements. He proposed that molecules could not only move translationally, i.e. in a straight line, but also vibrationally and rotationally as well.

Jyoti Asundi (34:55)
Yes.

Aarati Asundi (34:56)
He also found that molecules move incredibly fast. 

Jyoti Asundi (35:00)
Mmm.

Aarati Asundi (35:01)
So I didn't know this at all. It really blew my mind. So for example, the air that is around you right now is made up of tons of different molecules. We have nitrogen, oxygen, hydrogen. We have all these things. At room temperature, according to Rudolf Clausius's equations, on average, each molecule is moving at 500 meters a second or over 1,100 miles per hour.

Jyoti Asundi (35:30)
No way! Oh wow!

Aarati Asundi (35:31)
Isn't that insane? They're moving so incredibly fast.

Jyoti Asundi (35:36)
Yes.

Aarati Asundi (35:38)
But when Clausius proposed this, because he's like, all the math that I'm doing points to these numbers that are just incredibly high, people were like, how is that even possible?

Jyoti Asundi (35:51)
Impossible, impossible. Yeah.

Aarati Asundi (35:52)
Yeah. Because if molecules were really moving that fast, every time that something happened in one part of the room, like if there was smoke or perfume or something in one part of the room, it would immediately fill the whole room. It would be everywhere immediately. 

Jyoti Asundi (36:08)
Dispersed very quickly. Yes.

Aarati Asundi (36:10)
Yeah, like instantaneously. And we know that that's not the case. We know it kind of diffuses really slowly throughout the whole room.

Jyoti Asundi (36:19)
Yeah.

Aarati Asundi (36:20)
Rudolf was like, great question. I wonder why that is. And his answer was that even though the molecules are moving very fast, they aren't moving very far.

Jyoti Asundi (36:32)
So they're kind of dancing around in place?

Aarati Asundi (36:35)
Not, not dancing around in place, but there are billions of molecules in the air, all moving in random directions and bouncing off of each other. So if you spray perfume or add some smoke into this room, these molecules join this like madly jostling crowd of molecules that are all bumping into each other randomly, changing direction like crazy.

Jyoti Asundi (37:01)
Yes.

Aarati Asundi (37:01)
And so because of that, they're like expending a lot of energy to not move very far. 

Jyoti Asundi (37:07)
Make sense. Yes. 

Aarati Asundi (37:07)
And so it takes a long time for them to actually get...

Jyoti Asundi (37:10)
Yeah, there is nowhere to go because there is so much there is there are so many molecules all over the place. It's like being caught in one of those really tight situations like a stampede or like in a big hall where there are so many people and you you can jump up and down all you want but there's nowhere to go. 

Aarati Asundi (37:31)
There's nowhere to go. Yeah. So you got to move slowly even if you are on a sugar high and going nuts.

Jyoti Asundi (37:36)
Absolutely.

Aarati Asundi (37:38)
So Rudolf came up with a new term called the mean length of path, which is how far on average can a molecule move before its center of gravity comes into the sphere of action of another molecule.

Jyoti Asundi (37:54)
Ha.

Aarati Asundi (37:55)
That is going to be important in our next episode so put a pin in that.

Jyoti Asundi (38:00)
So that's the building block. Just cycle was important for Clausius, same way this mean path length is going to be important for the next person we are going to do. 

Aarati Asundi (38:12)
Exactly. Yeah. In 1869, Rudolf accepted a chair position at the University of Bonn in Prussia, which was a large northern German state. However, just when he's soaring high with his academic achievements, the Franco-Prussian war broke out. I'm not going to get too much into it, there are entire history documentaries, you know, that are...

Jyoti Asundi (38:40)
Talk about... Yeah.

Aarati Asundi (38:40)
...dedicated to the Franco-Prussian War and what exactly happened and why. But just really briefly, two years earlier, Queen Isabella II of Spain was overthrown and a man named Leopold of Hohenzollern, who was a relative of the King of Prussia was chosen to succeed her. 

Jyoti Asundi (39:01)
Okay.

Aarati Asundi (39:02)
But France, which sat in the middle of Spain and Prussia didn't like this because they already had tension with Prussia. And now if Spain became a strong ally of Prussia through this succession, they would be surrounded basically. 

Jyoti Asundi (39:17)
Yes, yes.

Aarati Asundi (39:19)
So then one thing led to another. There was like some, you know, sabotage intentional misleading of people and France ended up declaring war on Prussia.

Jyoti Asundi (39:31)
Okay so that causes the Franco-Prussian war.

Aarati Asundi (39:34)
Yes. Rudolf was 48 by this time, and so he was too old to be in combat. 

Jyoti Asundi (39:40)
That's good.

Aarati Asundi (39:41)
Yeah, but Rudolph's brother wrote "His burning patriotism did not permit him to stay idle at home during the War of 1870 to 71. He undertook the leadership of an ambulance corps, which he formed of Bonn students. At the great battles of Vionville and Gravelotte he helped carry the wounded from battle and to lessen their suffering." 

Jyoti Asundi (40:05)
Oh wow, what a noble guy.

Aarati Asundi (40:08)
Yeah. And even more noble is that I read that it didn't matter who was wounded. If it was a Prussian person or a French person, he just got them off the battlefield and made sure that....

Jyoti Asundi (40:19)
You are a human being and... lessen the suffering of humanity. Wow, he's a noble soul, beautiful.

Aarati Asundi (40:23)
Yes, very much. During the battle, though, Rudolph was wounded in the leg, which left him with a painful disability that he suffered with for the rest of his life.

Jyoti Asundi (40:35)
That's sad.

Aarati Asundi (40:36)
But he did win the Iron Cross in 1871 for his bravery.

Jyoti Asundi (40:40)
Okay.

Aarati Asundi (40:42)
His patriotism was tested again, this time more scientifically, when a Scottish mathematician and physician, Peter Guthrie Tait wrote an extremely pro-British review of the thermodynamics work that was being done by other British physicists like William Thompson and James Maxwell. 

Jyoti Asundi (41:02)
Okay. When you say pro-British what you mean is that he was expounding on the accomplishments of the British scientists, the findings of the British scientists and basically saying that's it. They're the best thing since sliced bread kind of thing. And then everybody else can a nap kind of thing.

Aarati Asundi (41:21)
Exactly. Yeah. He was like, look at all this fantastic work. It's brilliant.

Jyoti Asundi (41:25)
Yes got it.

Aarati Asundi (41:27)
And Rudolph was like, hey, you British only trying to take more credit than you should for some of your theories, because us Germans did something too. But also, you're misinterpreting... like when you do talk about my work, you're misinterpreting my work and making it, you know, seem like I got things wrong when you're the one who's getting things wrong, you know?

Jyoti Asundi (41:50)
Got it, got it, uh-huh, uh-huh.

Aarati Asundi (41:52)
So Rudolph wrote to James Maxwell because of this Tait person, Tait was basically saying, Maxwell is so wonderful. He wrote all this stuff about heat and work and energy. And, you know, contrast that with Rudolph Clausius, who has these other ideas about heat and work and energy. Rudolph Clausius is totally wrong and James Maxwell is the best and all of that. 

Jyoti Asundi (42:16)
So Rudolph is directly approaching Maxwell and saying, cut this person out. Let's talk this out.

Aarati Asundi (42:23)
Rudolph is like, know, Tait has compared our work. And actually, if you look at that direct comparison, you're wrong. Like James Maxwell, you're wrong. This guy is thinking that I'm wrong. And he's saying that British people are great and British scientists are great. But actually, you're the one, James Maxwell, who's wrong. And let me show you. And James Maxwell is like, "Oh you're right. I am wrong." You know? 

Jyoti Asundi (42:52)
Oh wow, wow, that's...great minds man. 

Aarati Asundi (42:56)
Yeah.

Jyoti Asundi (42:58)
Almost unheard of in today's world. In today's world it's all about doubling down and sticking to your ideas no matter who proves them wrong. Wow, wow, nice.

Aarati Asundi (43:06)
Yeah, I almost got this impression of Tait being this like, screaming, petulant little like child.

Jyoti Asundi (43:12)
Yes, troublemaker. Yeah, instigate...

Aarati Asundi (43:13)
And then the two parents are like, shh, we're talking, you know? 

Jyoti Asundi (43:17)
Yeah, yeah, let's figure this out. Yes.

Aarati Asundi (43:19)
Yeah, the two level-headed adults are like, okay, you know what, actually in all of that rambling, the child did make a good point. You know, like, let's talk about that. Yes.

Jyoti Asundi (43:27)
Yes, we should compare them and figure out who is right and actually the child got it wrong. You are right after all. Wow, nice, nice. So wise, so mature.

Aarati Asundi (43:39)
So James Maxwell fixed his misconceptions in the next edition of his book. But Tait continued to somehow misunderstand or completely ignore Rudolf Clausius' work, which ticked him off a lot. And so he spent a lot of time writing to publishers and magazines calling out Tait's errors.

Jyoti Asundi (43:59)
Okay.

Aarati Asundi (44:00)
After this, the details of his life get a bit scarce. We know that he was spending a lot of time calling out Tait's errors. In 1875, Rudolph's wife, Adelheid, sadly died giving birth to their sixth child. 

Jyoti Asundi (44:17)
Oh okay.

Aarati Asundi (44:19)
So because of this, Rudolph stepped back from his work to become the primary caregiver to his children.

Jyoti Asundi (44:25)
Wow and this is he's you said he's he was already like 40 something 48 or something at this point.

Aarati Asundi (44:31)
He's 48 during the Franco-Prussian war.

Jyoti Asundi (44:34)
Yeah, and now he's older he's probably closer to work somewhere in the mid 50s now. 

Aarati Asundi (44:38)
Fifties, yeah, mid 50s now. Mm-hmm. He continued to teach, but he was no longer able to contribute new ideas on thermodynamics. And after this, there actually wasn't much information about who Rudolph was as a person. So when you take away his scientific achievements and try to just look for information about Rudolph himself and his personality his hopes and dreams and stuff like that,

Jyoti Asundi (45:06)
Yeah.

Aarati Asundi (45:06)
We actually don't know much about it. Some historians think that maybe it's because he was a bit more on the quiet side. His son wrote that, "The most principal trait in my father's character was without a doubt the splendid truthfulness of his nature."

Jyoti Asundi (45:22)
A man of integrity.

Aarati Asundi (45:24)
Mm-hmm. And his brother said that he was a man of "rare modesty".

Jyoti Asundi (45:31)
Brilliant but modest.

Aarati Asundi (45:33)
Yes. But we also have a reference from one of Rudolph's students who refers to him as "that old grouch". Yeah. Although I have to say I'm not really sure when that was written, so it could have been after he got his painful war wound...

Jyoti Asundi (45:49)
And also the student could be a disgruntled guy. You know, one disgruntled student does not a reputation make.

Aarati Asundi (45:57)
Yes, that's true. Yeah. But I was like, you know, later in his life, he did have a bit to be grumpy about. He's got this painful war wound. He's getting irritated by Tait's misconceptions. And he's a single father of six kids. Yeah.

Jyoti Asundi (46:08)
Yes, he's lost his wife. Yes. He has earned his- if he was grumpy, then he earned it. He earned it. He earned the right to be grumpy. Yeah.

Aarati Asundi (46:16)
Yep, yeah, if he was a bit short with you, it's like maybe he just didn't have the time. He didn't have the time to deal with you. Yeah.

Jyoti Asundi (46:22)
Yeah, absolutely.

Aarati Asundi (46:25)
In 1886, Rudolf got married to his second wife, Sophie Sack, and has one more son with her. However, two years later, in 1888, Rudolf passes away at the age of 66 of unknown causes.

Jyoti Asundi (46:40)
Oh wow.  Oh but he did marry so late, he marries at 64 to his second wife and has a son at the age of 64.

Aarati Asundi (46:50)
And again, it's just like we don't have the details. I've tried looking up who Sophie Sack was and like her background. Came up empty. You know, I tried looking into what happened to Rudolph. Why did he pass away? Don't know. No one seems to know. So there's just really this dearth of information about him personally.

Jyoti Asundi (47:10)
But he came up with the first two law of thermodynamics and that is such a huge deal. Plus he's sort of starting to toy with the idea of how much can a molecule actually move? How much can the path length really be considering the amount of interference that it's going to face from other molecules who are also jostling around in the same place.
So he has these multiple excellent concepts. So then people are so focused on what he left in terms of scientific discovery that I can well see, especially with his own modesty and integrity. He's like, ⁓ let the light shine on the work and not on my own personal life.

Aarati Asundi (47:55)
Well, there was actually a really good quote about this from a book called Great Physicist from Galileo to Hawking by William H. Crooper. And he wrote about Rudolf Clausius, "This is an impressive story, but as a story, it's simply because we still do not know the main character. Most of us would consider it a great misfortune if we knew no more about Cézanne, Flaubert and Wagner, say, than what they put on canvas or paper or in a musical score. Clausius, their contemporary and equal as a creative genius has been taken from us as a human being in this way. We should mourn the loss."

Jyoti Asundi (48:40)
Oh wow. That's a good thought. Like yeah you need to know who the person is behind that discovery.

Aarati Asundi (48:47)
Yeah.

Jyoti Asundi (48:48)
We know him more one-dimensionally then. Because you're only knowing him through the dimension of his work in physics and thermodynamics.

Aarati Asundi (48:56)
Yeah. And it's like, can you imagine some great artists like Pablo Picasso or Beethoven, and all you had of them was their artwork or their music, and you knew nothing about them as a person or what inspired them or anything like that. So yeah.

Jyoti Asundi (49:10)
Yeah. Yeah, that would be a great loss to not understand where the work originated from.

Aarati Asundi (49:17)
Yeah. Yeah. So that is part two of our inadvertent totally not planned series on thermodynamics and physics. 

Jyoti Asundi (49:27)
Oh but this is fascinating, absolutely fascinating. And you're doing such a good job of leading me through the science. It's like I can see the building blocks all stacking up to create what we know today. So excellent. 

Aarati Asundi (49:41)
I hope so. I hope I'm getting it right. People out there are very, very good about letting me know when I made a mistake, and I appreciate that.

Jyoti Asundi (49:50)
Absolutely. Yeah, any mistakes in the science, any mistakes in the pronunciations, we welcome all corrections.

Aarati Asundi (49:57)
Yeah, we're here to learn too. So let us know. It's a two-woman team here. We don't have a big team. So you're our team.

Jyoti Asundi (50:05)
I'm learning a lot. I'm learning a lot. So I appreciate this opportunity to be here.

Aarati Asundi (50:11)
Awesome. Great. Well, we will see you next time in part three, which is the one that Arun actually wanted me to do and started this whole thing off with.

Jyoti Asundi (50:22)
And that will be the grand finale episode for the year 2025. 

Aarati Asundi (50:27)
Right, yeah, we're at the end, almost at the end.

Jyoti Asundi (50:30)
You will end the year with the finale for this trilogy.

Aarati Asundi (50:34)
It's very fitting. It's fitting in every way.

Jyoti Asundi (50:36)
It's beautifully planned out. Unplanned. 

Aarati Asundi (50:38)
Yeah, totally planned. Totally planned. Yeah.

Jyoti Asundi (50:40)
Yeah. Unplanned but sitting out so beautifully.

Aarati Asundi (50:46)
Thanks for listening. If you have a suggestion for a story we should cover or thoughts you want to share about an episode, reach out to us at smartteapodcast.com. You can follow us on Instagram, TikTok, and Blue Sky @smartteapodcast and listen to us on Spotify, Apple Podcasts, YouTube, or wherever you get your podcasts. And leave us a rating or comment. It helps us grow. New episodes are released every other Wednesday. See you next time.