32
R. Barrett and P. P. Delsanto
We never have a situation where heat flows in the other direction, thereby
increasing the temperature differential between the gases in the two flasks.
If we consider this situation from a microscopic point of view, molecules
in the hot flask are travelling on the average faster than those in the cold flask.
The interconnecting tube enables the molecules to mix and collide with each
other, with the result that on average the molecules of hot gas lose energy and
those of cold gas gain energy, until the temperature difference between the
two flasks vanishes. The Second Law states this principle formally, i.e. that
we never expect the temperature difference between the flasks to increase.
Such an action would be equivalent to replacing the disorder of completely
mixed up gases with a situation where there are more hot molecules in one
flask than in the other. The latter situation is less disordered than the first, a
violation of the first statement of the Second Law.
Imagine now that we have a minimal amount of gas (very few molecules)
distributed between the two interconnected flasks so that the temperatures in
the two flasks are the same. It is quite possible in this case that random collisions might produce a situation whereby, for a while, more hot gas molecules
are in one flask than the other, and we would have a temporary violation of
the Second Law.
We can draw an analogy with the tossing of a coin. On the average we
expect as many heads as tails when we toss an unbiased coin. If we toss the
coin a million times, our expectation is that the number of heads will be
within about 0.1% of the number of tails. However, if we only have three
throws, the likelihood of all three producing the same result is reasonably
high (1 in 4). The Second Law is similar, in that it is a statistical one; i.e., it
applies very accurately when we have large numbers of molecules taking part
in the collision processes. In a situation where there are approximately 10 22
molecules in the two jars, the law is essentially exact.
Essentially exact, but not quite. We shall discuss the importance of this
difference in the next Chapter, where we seek further insight into the nature
of physical truth.
Let us return now to the main topic of this Section. Complexity is a relatively new field of study arising from a recognition that there are areas of
science, that are too complex to be tackled by the conventional bottom-up
methodology. A statistical approach is the only available way for some problems. An everyday example occurs in meteorology, where it is quite common
to read a weather forecast along the lines that the chance of rain tomorrow is
60%, with a 30% chance of an afternoon thunderstorm. This may be frustrating if one is planning a picnic and would like more certainty about what
R. Barrett and P. P. Delsanto
We never have a situation where heat flows in the other direction, thereby
increasing the temperature differential between the gases in the two flasks.
If we consider this situation from a microscopic point of view, molecules
in the hot flask are travelling on the average faster than those in the cold flask.
The interconnecting tube enables the molecules to mix and collide with each
other, with the result that on average the molecules of hot gas lose energy and
those of cold gas gain energy, until the temperature difference between the
two flasks vanishes. The Second Law states this principle formally, i.e. that
we never expect the temperature difference between the flasks to increase.
Such an action would be equivalent to replacing the disorder of completely
mixed up gases with a situation where there are more hot molecules in one
flask than in the other. The latter situation is less disordered than the first, a
violation of the first statement of the Second Law.
Imagine now that we have a minimal amount of gas (very few molecules)
distributed between the two interconnected flasks so that the temperatures in
the two flasks are the same. It is quite possible in this case that random collisions might produce a situation whereby, for a while, more hot gas molecules
are in one flask than the other, and we would have a temporary violation of
the Second Law.
We can draw an analogy with the tossing of a coin. On the average we
expect as many heads as tails when we toss an unbiased coin. If we toss the
coin a million times, our expectation is that the number of heads will be
within about 0.1% of the number of tails. However, if we only have three
throws, the likelihood of all three producing the same result is reasonably
high (1 in 4). The Second Law is similar, in that it is a statistical one; i.e., it
applies very accurately when we have large numbers of molecules taking part
in the collision processes. In a situation where there are approximately 10 22
molecules in the two jars, the law is essentially exact.
Essentially exact, but not quite. We shall discuss the importance of this
difference in the next Chapter, where we seek further insight into the nature
of physical truth.
Let us return now to the main topic of this Section. Complexity is a relatively new field of study arising from a recognition that there are areas of
science, that are too complex to be tackled by the conventional bottom-up
methodology. A statistical approach is the only available way for some problems. An everyday example occurs in meteorology, where it is quite common
to read a weather forecast along the lines that the chance of rain tomorrow is
60%, with a 30% chance of an afternoon thunderstorm. This may be frustrating if one is planning a picnic and would like more certainty about what