At the present time we are familiar enough with molecules to formulate the Second
Law entirely in relation to an intuitive perception of their behavior. It is easy to see that the
Second Law, as expressed in terms of heat flow in section 11, could be violated with some
cooperation from molecules.
Consider two systems each consisting of a fixed quantity of gas. At the boundary of
each system are rigid, impenetrable, and well insulated walls except for a metal plate made
of a good thermal conductor and located between the systems as shown in Figure 1. The gas
in one system is at a low temperature T1 and in the other at a higher temperature T2. In
terms of molecular behavior the
temperature difference is produced by different distributions of molecules among the
velocities in the molecular states of each system. The number of different velocities,
however, is so large that the high temperature system contains some molecules with lower
speeds than some molecules in the low temperature system and vice versa.
Now suppose we prepare some instructions for the molecules in each system as
shown on the signs in Figure 1. When following these instructions, only the high speed
molecules in the low temperature gas collide with molecules on the surface of the plate, give
up energy to them, and thus create on this surface a higher temperature than in the gas.
The boundary between the gas and the plate then has a temperature difference across it and,
according to our definition, the energy thus transported is heat. In the plate this becomes
thermal energy which is conducted through it because the molecules on its other surface are
at a lower temperature as a consequence of their energy exchanges only with the low speed
molecules in the adjacent high temperature gas system. This constitutes likewise a heat flow
into this system. The overall result is then the continuous unaided transfer of heat from a
low temperature region to one at a higher temperature, clearly the wrong direction and a
Second Law violation. The Second Law therefore, is related to the fact that in completely
isolated systems molecules will never of their own accord obey any sort of instructions such
as these.
Microstates in Isolated Systems
To explain why molecules always behave as though instructions of this type are
completely ignored, imagine that we have a fantastic camera capable of making a
multidimensional picture which could show at any instant where all the ultimate particles
in the system are located and reveal every type of motion taking place, indicating its
location, speed, and direction. Every type of distinguishably different action at any moment,
the vibration, twisting, or stretching within molecules as well as their translational and
rotational movements, would be identified in this manner for every molecule in the system.
This picture would thus be a photograph of what we have defined as an instantaneous
microstate of the system.
Now, instead of the instructions on the signs in Figure I, suppose we ask the
molecules to do everything they can do by themselves in a rigid walled and isolated
container where no external arranging or directing operations are possible. We will say,
"Molecules, please begin now and arrange yourselves in a sequence of poses for pictures
which will show every possible microstate which can exist in your system under the
restrictions imposed by your own nature and the conditions of isolation in the container".
If we expressed these restrictions as a list of rules to be followed in assigning molecules to various positions and motions, the list would appear as follows:
1. In distributing yourselves among the various positions and motions for each microstate
picture, do not violate any energy conservation laws. Consequently, because you are in
an isolated system the sum of all your individual translational, vibrational, and
rotational kinetic energies plus all your intermolecular potential energies must always
be the same and equal to the fixed total internal energy of the system.
2. Likewise, do not violate any mass conservation laws. There are to be no chemical
reactions among you so that the total number of individual molecules assigned must
always remain the same.
3. All of you must, of course, remain at all times within the container so the total volume
in which you distribute yourselves must be constant.
4. Do not violate any laws of physics applicable to your particular molecular species. You
must remember that no two of you can have all of your microstate position and motion
characteristics exactly the same otherwise you would have to occupy the same space at
the same time. Furthermore, do not be concerned that there might not be enough
different microstates available for each of you to have a different one. Although you are
numerous, the number of different possible position and motion values is even more
numerous, so that there will never be enough of you to fill all of them and many
possible values will be left unoccupied by a molecule in each picture for which you pose.
Law entirely in relation to an intuitive perception of their behavior. It is easy to see that the
Second Law, as expressed in terms of heat flow in section 11, could be violated with some
cooperation from molecules.
Consider two systems each consisting of a fixed quantity of gas. At the boundary of
each system are rigid, impenetrable, and well insulated walls except for a metal plate made
of a good thermal conductor and located between the systems as shown in Figure 1. The gas
in one system is at a low temperature T1 and in the other at a higher temperature T2. In
terms of molecular behavior the
velocities in the molecular states of each system. The number of different velocities,
however, is so large that the high temperature system contains some molecules with lower
speeds than some molecules in the low temperature system and vice versa.
Now suppose we prepare some instructions for the molecules in each system as
shown on the signs in Figure 1. When following these instructions, only the high speed
molecules in the low temperature gas collide with molecules on the surface of the plate, give
up energy to them, and thus create on this surface a higher temperature than in the gas.
The boundary between the gas and the plate then has a temperature difference across it and,
according to our definition, the energy thus transported is heat. In the plate this becomes
thermal energy which is conducted through it because the molecules on its other surface are
at a lower temperature as a consequence of their energy exchanges only with the low speed
molecules in the adjacent high temperature gas system. This constitutes likewise a heat flow
into this system. The overall result is then the continuous unaided transfer of heat from a
low temperature region to one at a higher temperature, clearly the wrong direction and a
Second Law violation. The Second Law therefore, is related to the fact that in completely
isolated systems molecules will never of their own accord obey any sort of instructions such
as these.
Microstates in Isolated Systems
To explain why molecules always behave as though instructions of this type are
completely ignored, imagine that we have a fantastic camera capable of making a
multidimensional picture which could show at any instant where all the ultimate particles
in the system are located and reveal every type of motion taking place, indicating its
location, speed, and direction. Every type of distinguishably different action at any moment,
the vibration, twisting, or stretching within molecules as well as their translational and
rotational movements, would be identified in this manner for every molecule in the system.
This picture would thus be a photograph of what we have defined as an instantaneous
microstate of the system.
Now, instead of the instructions on the signs in Figure I, suppose we ask the
molecules to do everything they can do by themselves in a rigid walled and isolated
container where no external arranging or directing operations are possible. We will say,
"Molecules, please begin now and arrange yourselves in a sequence of poses for pictures
which will show every possible microstate which can exist in your system under the
restrictions imposed by your own nature and the conditions of isolation in the container".
If we expressed these restrictions as a list of rules to be followed in assigning molecules to various positions and motions, the list would appear as follows:
1. In distributing yourselves among the various positions and motions for each microstate
picture, do not violate any energy conservation laws. Consequently, because you are in
an isolated system the sum of all your individual translational, vibrational, and
rotational kinetic energies plus all your intermolecular potential energies must always
be the same and equal to the fixed total internal energy of the system.
2. Likewise, do not violate any mass conservation laws. There are to be no chemical
reactions among you so that the total number of individual molecules assigned must
always remain the same.
3. All of you must, of course, remain at all times within the container so the total volume
in which you distribute yourselves must be constant.
4. Do not violate any laws of physics applicable to your particular molecular species. You
must remember that no two of you can have all of your microstate position and motion
characteristics exactly the same otherwise you would have to occupy the same space at
the same time. Furthermore, do not be concerned that there might not be enough
different microstates available for each of you to have a different one. Although you are
numerous, the number of different possible position and motion values is even more
numerous, so that there will never be enough of you to fill all of them and many
possible values will be left unoccupied by a molecule in each picture for which you pose.