KINETIC THEORY

                    1. INTRODUCTION

In this topic we will know about kinetics theory. Boyle discovered the law named after him in 1661. Boyle, Newton and several others tried to explain the behaviour of gases by considering that gases are made up of tiny atomic particles. The actual atomic theory got established more than 150 years later. Kinetic theory explains the behaviour of gases based on the idea that the gas consists of rapidly moving atoms or molecules. This is possible as the inter-atomic forces,which are short range forces that are important for solids and liquids, can be neglected for gases.

  The kinetic theory was developed in the nineteenth century by Maxwell, Boltzmann and others. It has been remarkably successful. It gives a molecular interpretation of pressure and temperature

of a gas, and is consistent with gas laws and Avogadro’s hypothesis. It correctly explains specific heat capacities of many gases. It also relates measurable properties of gases

such as viscosity, conduction and diffusion with molecular parameters, yielding estimates of molecular sizes and masses.

  2. MOLECULAR NATURE OF MATTER

Richard Feynman, one of the great physicist of 20th century considers the discovery that “Matter is made up of atoms” to be a very significant one. Humanity may suffer annihilation (due to nuclear catastrophe) or extinction (due to environmental disasters) if we do not act wisely. If that happens, and all of scientific knowledge were to be destroyed then Feynman would like the ‘Atomic Hypothesis’ to be communicated to the next generation of creatures in the

universe. Atomic Hypothesis: All things are made of atoms - little particles that move around in perpetual motion, attracting each other when they are a little distance apart,

but repelling upon being squeezed into one another.

Speculation that matter may not be continuous, existed in many places and cultures. Kanada in India and Democritus

in Greece had suggested that matter may consist  of indivisible constituents. The scientific ‘Atomic  Theory’ is usually credited to John Dalton. He  proposed the atomic theory to explain the laws of definite and multiple proportions obeyed by elements when they combine into compounds. 

The first law says that any given compound has,  a fixed proportion by mass of its constituents. 

The second law says that when two elements

form more than one compound, for a fixed mass  of one element, the masses of the other elements are in ratio of small integers. 

To explain the laws Dalton suggested, about

200 years ago, that the smallest constituents

of an element are atoms. Atoms of one element  are identical but differ from those of other  elements. A small number of atoms of each  element combine to form a molecule of the  compound. Gay Lussac’s law, also given in early  19th century, states: When gases combine  chemically to yield another gas, their volumes  are in the ratios of small integers. Avogadro’s  law (or hypothesis) says: Equal volumes of all 

gases at equal temperature and pressure have  the same number of molecules. Avogadro’s law, when combined with Dalton’s theory explains Gay Lussac’s law. Since the elements are often in the form of molecules, Dalton’s atomic theory can also be referred to as the molecular theory 

of matter. The theory is now well accepted by scientists. However even at the end of the 

nineteenth century there were famous scientists  who did not believe in atomic theory ! From many observations, in recent times we now know that molecules (made up of one or more atoms) constitute matter. Electron microscopes and scanning tunnelling microscopes enable us to even see them. The size of an atom is about an angstrom (10 ^-10 m). 

In solids, which are tightly packed, atoms are  spaced about a few angstroms (2 Å) apart. In liquids the separation between atoms is also about the same. In liquids the atoms are not as rigidly fixed as in solids, and can move around. This enables a liquid to flow. In gases the interatomic distances are in tens of angstroms. The average distance a molecule can travel without colliding is called the mean free path. The mean free path, in gases, is of the order of thousands of angstroms. The atoms 

are much freer in gases and can travel long

distances without colliding. If they are not

enclosed, gases disperse away. In solids and

liquids the closeness makes the interatomic force  important. The force has a long range attraction and a short range repulsion. The atoms attract when they are at a few angstroms but repel when they come closer. The static appearance of a gas is misleading. The gas is full of activity and the

equilibrium is a dynamic one. In dynamic

equilibrium, molecules collide and change their  speeds during the collision. Only the average  properties are constant. Atomic theory is not the end of our quest, but 

the beginning. We now know that atoms are not  indivisible or elementary. They consist of a  nucleus and electrons. The nucleus itself is made up of protons and neutrons. The protons and neutrons are again made up of quarks. Even quarks may not be the end of the story. There may be string like elementary entities. Nature always has surprises for us, but the search for 

truth is often enjoyable and the discoveries

beautiful. In this chapter, we shall limit ourselves  to understanding the behaviour of gases (and a little bit of solids), as a collection of moving molecules in incessant motion. 

        3. BEHAVIOUR OF GASES

Properties of gases are easier to understand than  those of solids and liquids. This is mainly  because in a gas, molecules are far from each other and their mutual interactions are negligible except when two molecules collide. Gases at low pressures and high temperatures much above that at which they liquefy (or solidify) approximately satisfy a simple relation 

between their pressure, temperature and volume  given by 

 

PV = KT 

for a given sample of the gas. Here T is the

temperature in kelvin or (absolute) scale. K is a  constant for the given sample but varies with the volume of the gas. If we now bring in the idea of atoms or molecules, then K is proportional to the number of molecules, (say) N in the sample. We can write K = N k . Observation tells us that this k is same for all gases. It is called Boltzmann constant and is denoted by k B.