"Oh, it was really neat at the lecture of Prof. Lenard yesterday, he is talking now about the kinetic theory of heat of gases; so, it turned out that the molecules of O move with a velocity of over 400 m per second, then the good prof. calculated and calculated, set up equations, differen., integrated, substituted and it finally turned out that even though these molecules do move with this velocity, they travel a distance of only 1/100 of a hairbreadth”

The student is referencing the kinetic theory of gases, which is a fundamental concept in thermodynamics and statistical mechanics. This theory describes how gases behave at the microscopic level, considering them as a large number of small particles (molecules), all of which are in constant, random motion.

In the kinetic theory of gases, temperature is related to the average kinetic energy of the gas molecules. In this case, the student is referring to a lecture by Prof. Lenard (likely Philipp Lenard, who was a German physicist and the winner of the Nobel Prize for Physics in 1905 for his research on cathode rays) where he mentions the high velocities of oxygen (O) molecules.

The velocity of 400 m/s is a typical average speed for molecules in a gas at room temperature. However, because these molecules are constantly colliding with each other and changing directions, their actual path or "mean free path" (the average distance a molecule travels before colliding with another molecule) is very small. That's what the student means by "they travel a distance of only 1/100 of a hairbreadth". The number is meant to illustrate just how short the mean free path is in comparison to the speeds at which the molecules are moving.

This explanation, delivered through complex calculations involving differential equations and integrations, is a key concept in the kinetic theory of gases, and forms the basis for our understanding of heat, temperature, and pressure in gases.

Thermodynamics (1824 - Present): The kinetic theory of gases offered a microscopic explanation for the macroscopic behaviors described by the laws of thermodynamics. The foundation of thermodynamics was laid by Sadi Carnot in the 1820s with the development of the Carnot cycle, and Rudolf Clausius and William Thomson (Lord Kelvin) later formulated the first and second laws of thermodynamics in the mid-19th century.

Statistical Mechanics (1860 - Present): The kinetic theory of gases was a pioneering concept in statistical mechanics, a branch of physics that uses statistical methods to explain the behaviors of a system of particles. James Clerk Maxwell and Ludwig Boltzmann were instrumental in the development of this field in the late 19th century.

Quantum Mechanics (1900 - Present): The kinetic theory of gases, coupled with the blackbody radiation problem, helped lead to the development of quantum mechanics. The classical kinetic theory couldn't explain certain experimental results related to blackbody radiation, leading to Max Planck's quantum hypothesis in 1900. This marked the beginning of quantum mechanics, with other major contributors including Albert Einstein, Niels Bohr, and Werner Heisenberg.

Heat Transfer and Fluid Dynamics (1800s - Present): The understanding of heat transfer modes (conduction, convection, and radiation) and the behavior of gases in fluid dynamics benefited from the kinetic theory of gases. The field of fluid dynamics was significantly developed by Claude-Louis Navier and George Gabriel Stokes in the 19th century, with the formulation of the Navier-Stokes equations.

Plasma Physics (1920s - Present): Kinetic theory is also essential in plasma physics, which deals with ionized gases. Irving Langmuir coined the term "plasma" in reference to ionized gas in the 1920s. The field has since become crucial in understanding phenomena such as nuclear fusion, solar winds, and auroras.