Modern Thermodynamics
- Chapter 1
1.6 An Introduction to Kinetic Theory of Gases
When Robert Boyle published his study on the nature of the "spring of the sir" (what we call pressure
today) and argued that heat was an "intense commotion of the parts", he did not know how pressure
actually arose. During the seventeenth century, a gas was thought to be a continuous substance. A
century later, Daniel Bernoulli (1700-1782) published the idea that the mechanism that caused pressure is
the rapid collisions of molecules with the walls of the container5. In his 1738 publication,
Hydrodynamica, Bernoulli presented his calculation of the average force on the container walls due to
molecular collisions and obtained a simple expression for the pressure: p=(mnv2avg/3), in which m is the
molecular mass, n is the number of molecules per unit volume and vavg is the average speed of molecules.
At that time, no one had any idea how small gas molecules were or how fast they moved, but Bernoulli's
work was an important step in explaining the properties of a gas in terms of molecular motion. It was the
beginnings of a subject that came to be known as the kinetic theory of gases.
Kinetic theory of gases was largely developed in the late nineteenth century. Its goal was to
explain the observed properties of gases by analyzing the random motion of molecules. Many quantities
such as pressure, diffusion constant and the coefficient of viscosity could be related to the average speed
of molecules, their mass, size, and the average distance they traversed between collisions (called mean
free path). As we shall see in this section, the names of James Clerk Maxwell (1831-1879) and Ludwig
Boltzmann (1844-1906) are associated with some of the basic concepts in this field, while, as is often the
case in science, several others contributed to its developmen4,5. In this introductory section we shall deal
with some elementary aspects of kinetic theory such as mechanism that causes pressure and the relation
between average kinetic energy and temperature.
Kinetic Theory of Pressure
As Daniel Bernoulli showed, using the basic concepts of force and randomness, it is possible to relate the
pressure of a gas to molecular motion: pressure is the average force per unit area exerted on the walls by
colliding molecules.
We begin by noting some aspects of the random motion of molecules. First, if all directions have
the same physical properties, we must conclude that motion along all directions are equally probable: the
properties of molecules moving in one direction will be the same as the properties of molecules moving
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