Thermodynamics: Change in entropy of a falling ball

In summary, in this conversation, the discussion revolves around determining the change of entropy in a closed isolated system where a rigid ball is released from a certain height and falls to a lower height. The conversation also touches on the reversibility of this process and the effects of potential energy and heat transfer. Despite some uncertainty and different opinions, it is suggested that the entropy does not change and the process is reversible, assuming that the change in potential energy is lost as heat to the surroundings.
  • #1
death_knight
3
0

Homework Statement


In a closed isolated system, a small rigid ball is held at height h1, which we will call state A. By remote control a pin is pulled and the ball is released. It falls to height h2, called state B. Calculate the change of entropy S of the system. Is it a reversible or irreversible process?


Homework Equations



Delta S = Delta Q/T

The Attempt at a Solution


My attempt is that since the system is isolated that means no heat is transferred and the entropy is not changed at all.

But again, since the position of the ball is now lowered, it also means it has lost some potential energy, so change in Q can be related to change in energy which can be mg(h1-h2), with T being constant. So am not sure which one is the right answer.

Also sometimes I think it is an irreversible process because external work will be needed to bring the ball back to its original height but then I also get confused that it might be reversible process because it's an closed isolated system.

Thanks for your help in advance!
 
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  • #2
The ball seems to be still falling at H2. In this case it would appear the since the ball can still do the same work it could at H1, I'd say the entropy is unchanged. If you said the ball bounced off the bottom, there'd be a little heat there and the ball would loose the ability to recoil back to H1. In that case you'd have an entropy increase.

It's reversible if the ball can bounce back up to H1. It's rigid so that might work. If the ball was made of clay-filled leather you'd imagine it would be quite irreversible.
 
  • #3
Antiphon said:
The ball seems to be still falling at H2. In this case it would appear the since the ball can still do the same work it could at H1, I'd say the entropy is unchanged. If you said the ball bounced off the bottom, there'd be a little heat there and the ball would loose the ability to recoil back to H1. In that case you'd have an entropy increase.

It's reversible if the ball can bounce back up to H1. It's rigid so that might work. If the ball was made of clay-filled leather you'd imagine it would be quite irreversible.

Well I thought, the ball kind of stays at the second position. I agree to your theory but again this notion of mechanical work done in this process bugs me a lot. What about the loss in potential energy of the ball?

Note: Note that height h1>h2, the initial height is greater than the final height.
 
  • #4
death_knight said:
Well I thought, the ball kind of stays at the second position. I agree to your theory but again this notion of mechanical work done in this process bugs me a lot. What about the loss in potential energy of the ball?

Note: Note that height h1>h2, the initial height is greater than the final height.
It is not a very good question because we don't know how the ball loses its energy. If it landed on a spring and the spring energy held by another pin at its maximum point, there would be no heat produced and no change in entropy. The ball could go back to its original height by releasing the spring. So it is reversible.

Having said that, I suspect that you are supposed to assume that the change in potential energy is lost as heat.

AM
 
  • #5
Andrew Mason said:
It is not a very good question because we don't know how the ball loses its energy. If it landed on a spring and the spring energy held by another pin at its maximum point, there would be no heat produced and no change in entropy. The ball could go back to its original height by releasing the spring. So it is reversible.

Having said that, I suspect that you are supposed to assume that the change in potential energy is lost as heat.

AM

Thanks Andrew!

So you suggest the answer would be that "Entropy doesn't change" and the process is "reversible"

Right? I am going to confirm that with the Teaching Assistant or the professor himself soon, and if I get something from them, I'll share here :)
 
  • #6
death_knight said:
Thanks Andrew!

So you suggest the answer would be that "Entropy doesn't change" and the process is "reversible"

Right? I am going to confirm that with the Teaching Assistant or the professor himself soon, and if I get something from them, I'll share here :)
No. I am not sure. I think the person who posed the question may want you to assume that the change in potential energy is transferred to the surroundings as heat, in which case, the entropy increases by the amount mg(h1-h2)/T where T is the ambient temperature.

AM
 
Last edited:

1. What is the change in entropy of a falling ball?

The change in entropy of a falling ball is a measure of the disorder or randomness of the system as it moves from a higher energy state to a lower one. It is represented by the symbol ΔS and is typically expressed in units of joules per kelvin (J/K).

2. How is entropy related to thermodynamics?

Entropy is one of the fundamental concepts in thermodynamics, which is the study of energy and its transformations. It is closely related to the second law of thermodynamics, which states that the total entropy of a closed system will always increase over time.

3. Does the change in entropy of a falling ball always increase?

According to the second law of thermodynamics, the change in entropy of a falling ball will always increase. This is because as the ball falls, it loses potential energy and gains kinetic energy, resulting in a more disordered system with a higher level of entropy.

4. Can the change in entropy be negative?

In theory, the change in entropy can be negative if the system is able to become more ordered as it undergoes a process. However, in most cases, the change in entropy is positive because systems tend to become more disordered over time.

5. How does gravity affect the change in entropy of a falling ball?

Gravity plays a crucial role in the change in entropy of a falling ball. As the ball falls, it experiences a force due to gravity, which causes it to accelerate and gain kinetic energy. This increase in kinetic energy leads to a corresponding increase in entropy, as outlined by the second law of thermodynamics.

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