2 The Meaning of Understanding
31
Impressive as the space program undoubtedly was, the score or so of interacting bodies involved in these calculations is negligible compared with the
approximately 10 22 molecules 4 in a jar of air. Numerical methods cannot
provide a way to handle the interactions of this number of molecules, and
physicists have been forced to resort to a statistical approach.
In “Statistical Mechanics”, the behaviour of molecules is only considered
en masse. The bulk properties of matter are studied, and concepts such as
temperature and pressure introduced, which arise from the average behaviour
of large numbers of molecules. Temperature is related to the average energy
of motion of the molecules, and pressure to their impact on the walls of the
vessel containing them. New laws of physics are formulated which connect
these bulk properties. For instance, increasing the pressure of a gas confined
in a flask results in a proportional increase in the temperature of the gas. 5
This relationship was first discovered by Joseph Louis Gay-Lussac in 1809.
There is a difference between these “statistical” laws and the more fundamental laws describing the interaction of particles. The former may in
principle be derivable from the latter, and as such may not be considered
to be basic laws of physics at all. Although this may be true in some cases, in
most scenarios such derivations are not possible because of the complexity of
the interactions and the huge numbers of particles involved.
The science of Thermodynamics was developed in the 19th Century, and
was motivated by a desire to increase the power and efficiency of steam
engines. Its laws do not relate to interactions between individual particles, but
rather involve higher level concepts, such as heat, temperature and entropy.
The term “entropy” has been coined for a measure of the disorder of a system.
The universe is analogous to a child’s playroom, where the toys start out in
the morning neatly arranged on shelves and in boxes, but at the end of the
day have become strewn randomly over every horizontal surface. Left to itself,
nature tends to the state of maximum disorder. This tendency is expressed in
what is known as “the Second Law of Thermodynamics”, i.e. “entropy tends
to a maximum.” (A popular skit on this topic is discussed in Appendix 2.2.)
The Second Law is often stated in the alternative form: “heat cannot spontaneously flow from a colder location to a hotter location.” If we consider two
flasks of gas, one at a higher temperature than the other, and connect them
together with a tube, heat is gradually transferred from the hot flask to the
cold one, stopping when the gas in both flasks is at the same temperature.
4 Scientific notation for 1 followed by 22 zeroes.
5 The temperature in this case is the absolute temperature, which is measured in the Kelvin scale. The
absolute temperature is obtained by adding 273.15 to the temperature in degrees Celsius.
31
Impressive as the space program undoubtedly was, the score or so of interacting bodies involved in these calculations is negligible compared with the
approximately 10 22 molecules 4 in a jar of air. Numerical methods cannot
provide a way to handle the interactions of this number of molecules, and
physicists have been forced to resort to a statistical approach.
In “Statistical Mechanics”, the behaviour of molecules is only considered
en masse. The bulk properties of matter are studied, and concepts such as
temperature and pressure introduced, which arise from the average behaviour
of large numbers of molecules. Temperature is related to the average energy
of motion of the molecules, and pressure to their impact on the walls of the
vessel containing them. New laws of physics are formulated which connect
these bulk properties. For instance, increasing the pressure of a gas confined
in a flask results in a proportional increase in the temperature of the gas. 5
This relationship was first discovered by Joseph Louis Gay-Lussac in 1809.
There is a difference between these “statistical” laws and the more fundamental laws describing the interaction of particles. The former may in
principle be derivable from the latter, and as such may not be considered
to be basic laws of physics at all. Although this may be true in some cases, in
most scenarios such derivations are not possible because of the complexity of
the interactions and the huge numbers of particles involved.
The science of Thermodynamics was developed in the 19th Century, and
was motivated by a desire to increase the power and efficiency of steam
engines. Its laws do not relate to interactions between individual particles, but
rather involve higher level concepts, such as heat, temperature and entropy.
The term “entropy” has been coined for a measure of the disorder of a system.
The universe is analogous to a child’s playroom, where the toys start out in
the morning neatly arranged on shelves and in boxes, but at the end of the
day have become strewn randomly over every horizontal surface. Left to itself,
nature tends to the state of maximum disorder. This tendency is expressed in
what is known as “the Second Law of Thermodynamics”, i.e. “entropy tends
to a maximum.” (A popular skit on this topic is discussed in Appendix 2.2.)
The Second Law is often stated in the alternative form: “heat cannot spontaneously flow from a colder location to a hotter location.” If we consider two
flasks of gas, one at a higher temperature than the other, and connect them
together with a tube, heat is gradually transferred from the hot flask to the
cold one, stopping when the gas in both flasks is at the same temperature.
4 Scientific notation for 1 followed by 22 zeroes.
5 The temperature in this case is the absolute temperature, which is measured in the Kelvin scale. The
absolute temperature is obtained by adding 273.15 to the temperature in degrees Celsius.