Reading Quiz

Question 1:

In your own words, describe the fundamental assumption of statistical mechanics.

Answer:

According to the book, p. 57, it is the assumption that in an isolated system at thermal equilibrium, all accessible microstates are equally probable. Your responses are below.
  1. When a system is in thermal equilibrium, all possible arrangements (microsystems) of the system occur with the same probability. In other words, given enough time, all possible arrangements of a system in thermal equilibrium, all the arrangements will occur.
  2. The fundamental assumption of statistical mechanics is that all microstates are equally likely.
  3. The assumption is that all microstates of a system are equally likely. Thus the state of the system on a microscopic level is essentialy random.
  4. All microstates are equally probable in a system at thermal equilibrium as long as no outside sources act on the system.
  5. For a closed thermal system at equilibrium, a given microstate is as likely to occur as any other microstate.
  6. The fundamental assumption of statistical mechanics assumes that everything that can happen is equally likely to happen on a microstate level.
  7. Every individual microstate (that is the detailed description of every molecule) is equally likey. There exists no configuration that is more probable than any other.
  8. All microstates have an equal probability of occuring.
  9. All microstates in a system are equally likely to be observed. Said differently, no preference exists for one microstate over another microstate.
  10. In any system, no matter how many microstates there are, each microstate is equally as likely as any other microstate.
  11. All microstates are equally probable.

Question 2:

What does the Second Law of Thermodynamics mean in terms of multiplicity?

Answer:

If you prepare a system in a macrostate with a relatively low multiplicity, it will tend to "move" towards a macrostate of relatively high multiplicity. The spontaneous flow of energy stops when a system is at or near its most likely macrostate.
  1. That spontaneous flow of energy (in the form of heat) will stop when the energetical macrostate is at its most probable. In other words, spontaneous flow of energy only occurs if it increases the multiplicity.
  2. The Second Law of Thermodynamics means that systems move toward macrostates with higher multiplicities.
  3. That the system goes towards the Macrostate with that is most likely, thus the state that has the highest multiplicity.
  4. The spontaneous flow of energy stops when the system is at or near the macrostate with the greatest multiplicity.
  5. A system will equilibrate towards the the macrostate with the largest multiplicity.
  6. A system will always tend to go towards its greatest multiplicity value.
  7. A system will most likely move to the macrostate with the largest multiplicity.
  8. Energy will copntimue to flow in a system until the system reaches its highest multiplicity.
  9. When a system reaches the macrostate with the highest multiplicity, the spontaneous flow of energy stops. Further energy transfer requires the input of heat or work.
  10. As a system approaches a macrostate with a higher multiplicity, the energy flow begins to slow down.
  11. Over time, a system will evolve toward macrostates with a higher multiplicity.

Question 3:

Why might we say that the Second Law of Thermodynamics is not a fundamental physical law?

Answer:

Because it's simply a (very strong) statement about probabilities: systems tend to go to their most probable state.
  1. A fundamental law usually says concrete and decisive about what a system can or cannot do physically using physical properties of a system, it seems that in this sense it isn't fundamental since multiplicity isn't exactly a physical property of a system.
  2. It's more like a statement of what probability does - the more probable a state, the more likely systems will move towards it.
  3. This is not a fundamental physical law because we are not proving anything here. These are assumptions that nature tends to follow, and they describe perfectly well what happens. However they are based on probabilities and statistics not pure proofs.
  4. It is more like a very strong statement about probabilities because we only have very good approximations which tell us that this is the case.
  5. Although the second law is overwhelmingly probable, there is still an infintesimal probability that a system will not obey it.
  6. It's a statement of something that is overwhelmingly likely, but it isn't something that we can prove for certain.
  7. It doesn't tell us what happens all of time, just most of the time.
  8. The Second Law does not actually predict anyting about the system, it instead gives a very powefrul prediction of the probabilities of the outcomes of measurements of the system.
  9. It is based upon statistical calculations and not upon physical measurements.
  10. 1. It's based on the fundamental assumption of statistical mechanics. 2. It can't be proven. 3. For systems of very few particles it is hard to show this law applies.
  11. The second law is basically a statement of probability - there is no justification for saying that energy has to or always flows toward the more likely macrostate by some mathematical reasoning, it just happens to be the most probable outcome.

Question 4:

What material from the reading or previous classes would you like me to go over in more detail?

Answer:

Your responses below.
  1. nope
  4. Homework problem 2.4 was confusing. We dealt with problems where only two outcomes were possible with coins and they were just as likely with each subsequent roll. The poker hand is a different case.
  5. none.
  6. Do we know the number of macrostates of energy available in the universe? Have some of these become inaccessible as the universe cooled?
  8. Nothing that I can think of.
  10. Nothing really.
  11. This stuff in particular is pretty straightforward and familiar.