History - Evolution of ideas in the field of thermodynamics (statistics in mechanical and gas dynamics)

  • #1
Ker_
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Hi,
I have a question regarding the evolution of idea in the field of thermodynamics.
Boltzmann is genereally credited with the notion of stasticis and it's relation to entropy. However, Boltzmann was inspired by the work of Maxwell (who himself followed the conceptual models of Bernoullli for the gas pressure). So why do we credit Boltzmann and not Maxwell for the "paternity" of statistics in mechanical and gas dynamics? What contribution did Boltzmann made that was so determinant?

Also, the equation s=klog(w) that is attributed to boltzmann... wasn't it Max Planck who actually wrote it down when working on his black body problem?

Thanks for helping me!
 
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  • #2
I think Planck used the idea in a specific situation whereas Boltzmann used the idea in the general situation, providing a statistical explanation of the 2nd Law.
 
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  • #4
Ker_ said:
Hi,
I have a question regarding the evolution of idea in the field of thermodynamics.
Boltzmann is genereally credited with the notion of stasticis and it's relation to entropy. However, Boltzmann was inspired by the work of Maxwell (who himself followed the conceptual models of Bernoullli for the gas pressure). So why do we credit Boltzmann and not Maxwell for the "paternity" of statistics in mechanical and gas dynamics? What contribution did Boltzmann made that was so determinant?

Also, the equation s=klog(w) that is attributed to boltzmann... wasn't it Max Planck who actually wrote it down when working on his black body problem?

Thanks for helping me!
I'd say the very first having an idea of "kinetic theory" was Daniel Bernoulli, which has been taken up in more generality by Maxwell, as you say. Boltzmann's merit is to have derived the transport equation named after him and the discovery of the "H-theorem" ("Eta theorem"), which in modern formulation says that macroscopic entropy doesn't decrease, and equilibrium has thus to be a state of maximum entropy. The equation for the entropy in the microcanonial ensemble, ##S=-k \ln \Omega##, is indeed due to Max Planck.

The general equation, of course is (for classical statistics),
$$S=-k \int \mathrm{d}^3 x \mathrm{d}^3 p/h^3 f \ln(f/h^3).$$
Of course, Boltzmann couldn't know the quantum-theoretical choice of the "elementary one-particle phase-space cell" of volume ##h^3##, with ##h## Planck's quantum of action.
 
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  • #5
Ker_ said:
Hi,
I have a question regarding the evolution of idea in the field of thermodynamics.
Boltzmann is genereally credited with the notion of stasticis and it's relation to entropy. However, Boltzmann was inspired by the work of Maxwell (who himself followed the conceptual models of Bernoullli for the gas pressure). So why do we credit Boltzmann and not Maxwell for the "paternity" of statistics in mechanical and gas dynamics? What contribution did Boltzmann made that was so determinant?

Also, the equation s=klog(w) that is attributed to boltzmann... wasn't it Max Planck who actually wrote it down when working on his black body problem?

Thanks for helping me!

"Maxwell and Boltzmann worked on the kinetic theory of gases at about the same time in a slightly different manner and they achieved largely the same results, – all except one! That one result, which escaped Maxwell,
concerned entropy and its statistical or probabilistic interpretation. It provides a deep insight into the strategy of nature and explains irreversibility. That interpretation of entropy is Boltzmann’s greatest achievement, and it places him among the foremost scientists of all times.
"

From the book "A History of Thermodynamics" by Ingo Müller
https://link.springer.com/book/10.1007/978-3-540-46227-9
 
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FAQ: History - Evolution of ideas in the field of thermodynamics (statistics in mechanical and gas dynamics)

What is the historical significance of the first law of thermodynamics?

The first law of thermodynamics, also known as the law of energy conservation, was formulated in the mid-19th century. It states that energy cannot be created or destroyed, only transformed from one form to another. This principle was crucial in unifying the study of heat, work, and energy, and it laid the foundation for modern energy management and engineering practices.

How did the concept of entropy evolve in thermodynamics?

The concept of entropy was introduced by Rudolf Clausius in the 1860s to quantify the amount of thermal energy not available to do work. It evolved further with Ludwig Boltzmann's statistical interpretation, which linked entropy to the number of microscopic configurations that correspond to a thermodynamic system's macroscopic state. This interpretation bridged the gap between macroscopic thermodynamic laws and microscopic statistical mechanics.

What role did James Clerk Maxwell play in the development of statistical mechanics?

James Clerk Maxwell made significant contributions to statistical mechanics, particularly through his development of the Maxwell-Boltzmann distribution in the 1860s. This distribution describes the statistical distribution of speeds of particles in a gas, providing a crucial link between the microscopic behavior of individual particles and the macroscopic properties of gases, such as temperature and pressure.

How did the study of gas dynamics influence thermodynamic theories?

The study of gas dynamics, especially through the kinetic theory of gases, played a pivotal role in shaping thermodynamic theories. The kinetic theory, developed by scientists like James Clerk Maxwell and Ludwig Boltzmann, provided a microscopic explanation for macroscopic thermodynamic properties. It explained how the motion and collisions of gas molecules lead to observable phenomena like pressure and temperature, thereby reinforcing the laws of thermodynamics with a solid molecular basis.

What impact did Ludwig Boltzmann's work have on modern thermodynamics and statistical mechanics?

Ludwig Boltzmann's work had a profound impact on both thermodynamics and statistical mechanics. He introduced the statistical interpretation of entropy and developed the Boltzmann equation, which describes the statistical behavior of a thermodynamic system out of equilibrium. His ideas provided a deep understanding of the microscopic foundations of thermodynamic laws and paved the way for the development of quantum mechanics and information theory.

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