Explanation of entropy only takes into account positions?

In summary, entropy is often defined as the log of the number of states that are macroscopically indistinguishable. This means that the entropy of a system depends on the number of positions all the particles in the system can be in. When a system moves to a state with equal numbers of particles, the entropy increases. However, it is important to note that entropy only considers the positions (or possible positions) of the particles, and not other factors such as momentum, temperature, and energy. This is because the number of macroscopically indistinguishable states does not take these factors into account. When two pieces of the same material at different temperatures are brought into contact, the system's entropy increases as heat is transferred from one
  • #1
dhruv8890
1
0
Hi,

I've read several times an explanation of entropy that describes it something like "log of the number of states that are macroscopically indistinguishable". So the entropy of a system depends on the number of positions all the particles in the system can be in - right?

If a system is like this picture:

EntropyBox.gif


and the system goes to a state where there are equal number of particles, the entropy will have increased. If that's correct then the entropy of the system only takes into account the positions (or possible positions) of the particles involved. My question is - why doesn't entropy take into account momentum, temperature, energy etc. That information isn't available in "the number of macroscopically indistinguishable states".

If 2 pieces of the same material, at different temperatures is brought into contact, the system's entropy increases as the heat is transferred from one piece to the other. How did the number of macroscopically indistinguishable states increase? The energy of the one piece went down as the other's went up - does this affect entropy?

Thank you and I appreciate the help,
Dhruv
 
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  • #2
Momentum is indeed taken into account. The state that the particle may fill is in 6-dimensional phase space (3 for position, 3 for momentum).
 

1. What is entropy and how is it related to position?

Entropy is a measure of the disorder or randomness of a system. In the context of thermodynamics, it is related to the positions of particles within a system. The more disordered or spread out the positions of the particles, the higher the entropy.

2. Why does the explanation of entropy only take into account positions?

This is because in the context of thermodynamics, entropy is primarily concerned with the number of microstates (possible arrangements of particles) that a system can have at a given energy level. It is easier to calculate and understand the positions of particles rather than their individual energies or velocities.

3. Is there a relationship between entropy and temperature?

Yes, there is a direct relationship between entropy and temperature. As the temperature of a system increases, the particles within it have more energy and are able to move more freely, increasing the number of possible arrangements and thus the entropy.

4. Why is entropy often referred to as a measure of disorder?

This is because as the number of possible arrangements of particles increases, the system becomes more disordered or random. Think of a deck of cards - when it is arranged in a specific order, it is considered orderly, but when the cards are shuffled and in any random arrangement, it is considered disordered.

5. Can entropy ever decrease?

In a closed system, entropy can never decrease. This is due to the second law of thermodynamics, which states that in any natural process, the total entropy of the universe will always increase. However, in open systems where energy can be exchanged with the surroundings, local decreases in entropy are possible as long as the overall entropy of the universe increases.

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