Thermodynamics and the Atomic and Molecular Structure of Matter 93
the gas increases (decreases) the number of molecules colliding with
the side and hence increases (decreases) the pressure. Subsequent
experimentation revealed that the product of the volume times the
pressure is directly proportional to the temperature. By considering
the gas at a fixed volume, we find that the pressure is proportional to
the temperature. If we extrapolate all the graphs of pressure versus
temperature at fixed volume to lower temperatures we find that the
pressure is zero when the temperature is –273.15° Centigrade. This
temperature represents absolute zero where all molecular motion ceases
and hence the pressure is zero. If we convert to the Kelvin scale of
temperature where –273.15° Centigrade is 0 Kelvin (and 0°^ Centigrade is
273.15 K) then for a fixed volume the pressure is directly proportional to
the temperature and approaches zero as the temperature also approaches
zero Kelvin.
The pressure of a gas at a fixed volume depends on the amount
of momentum transferred to the wall per unit time. The momentum
transferred per collision as mentioned above is proportional to the
momentum of the molecule. The rate at which the molecules strike the
wall on the other hand, is proportional to their velocity since the faster
they are moving the more likely it is they can reach the wall from any
given position in the gas. The pressure is therefore the product of the
molecule’s momentum times its velocity, which is just twice the kinetic
energy of the molecule and therefore the temperature is proportional to
the kinetic energy of the molecules.
The result explains why for a given substance that it takes a fixed
amount of energy to raise the temperature a fixed amount over a large
range of temperatures. The heat of a substance as predicted earlier by
Bacon is just the internal kinetic energy of the molecular or atomic
motion of the substance. The result that we derived for gases applies as
well to liquids and solids.
The molecular structure of matter also helps us to understand the
conduction of heat by solids. When two solids of different temperature
are in contact with each other the molecules of the hotter body are
moving faster than those of the cooler. As the faster moving molecules
collide with the slower moving ones they transfer some of their kinetic
energy to these molecules. This process goes on until eventually the two
bodies are at the same temperature. Convection is the process whereby
the transfer of heat takes place through the flow of a warm gas or liquid.
It is similar to conduction in that the molecules of the warmer body