Definition of a quasistaic process

[hasan_researc]

Wikipedia defines a quasistatic process as

"a thermodynamic process that happens infinitely slowly. However, it is very important of note that no real process is quasistatic. Therefore in practice, such processes can only be approximated by performing them infinitesimally slowly."

I do not properly understand the definition. My problem lies with the mathematics of infinity and infinitesimal in the definition.

Let's start with the prhase "a process that happens infinitely slow". Any process that starts to happen actually makes an increment (towards its final state) per unit of time. So, it will eventually reach its final state. But we would never want that to happen in reality because the process is meant to be completed in an infinite amount of time. So, the only logical conclusion is that the process 'does not happen at all'. Am I right?

Assuming that I am right, let's now turn to the sentence "in practice, such processes can only be approximated by performing them infinitesimally slowly". Now, an infinitesimal increment IS an increment towards the final state. That means eventually the system will reach its final state. So, in practice we can allow the process can happen infinitesimally for us to reach the final state.

Now here's the problem. Take a piece of unit length of some material and keep cutting it in half. Repeat the process for an infinite number of times and you should get an infinitesimal length. (Yes?) That implies that adding together infinitesimal amounts of lengths for an infinite number of times should give you the original finite length. (Or is it?)

If that is so, how does that fit in with the riginal discussion regarding a quasistatic process?

 

[peteratcam]

Wikipedia defines a quasistatic process as

"a thermodynamic process that happens infinitely slowly. However, it is very important of note that no real process is quasistatic. Therefore in practice, such processes can only be approximated by performing them infinitesimally slowly."

I do not properly understand the definition. My problem lies with the mathematics of infinity and infinitesimal in the definition.

Let's start with the prhase "a process that happens infinitely slow". Any process that starts to happen actually makes an increment (towards its final state) per unit of time. So, it will eventually reach its final state. But we would never want that to happen in reality because the process is meant to be completed in an infinite amount of time. So, the only logical conclusion is that the process 'does not happen at all'. Am I right?

Assuming that I am right, let's now turn to the sentence "in practice, such processes can only be approximated by performing them infinitesimally slowly". Now, an infinitesimal increment IS an increment towards the final state. That means eventually the system will reach its final state. So, in practice we can allow the process can happen infinitesimally for us to reach the final state.

Now here's the problem. Take a piece of unit length of some material and keep cutting it in half. Repeat the process for an infinite number of times and you should get an infinitesimal length. (Yes?) That implies that adding together infinitesimal amounts of lengths for an infinite number of times should give you the original finite length. (Or is it?)

If that is so, how does that fit in with the riginal discussion regarding a quasistatic process?

It is a crap definition. In thermodynamics, first you define the notion of equilibrium states, and get everyone to agree that if you leave most systems for long enough, in the presence of some constraints, they will come to equilibrium. Thermodynamic processes are defined in terms of the theoretical construct of equilibrium states.

A quasistatic process is a connected sequence of states, all of which are equilibrium states. (ie, could be realized as equilibrium states in the presence of appropriate constraints). You don't need a notion of time to define a quasistatic process, you just need a notion of equilibrium state.

Callen's thermodynamics book is excellent on this.

 

[hasan_researc]

Do you mean Thermodynamics and an Introduction to Thermostatistics by Herbert B Callen?

 

[peteratcam]

Yes, that book. It might not be the easiest read if you are learning thermodynamics for the first time, but it has the distinction (I think) of being the most cited thermodynamics textbook in the physics research literature.

Personally, I only started to feel I understood thermodynamics after reading Callen's book.

 

[hikaru1221]

Just some more opinions

I think it's like what peteratcam said earlier: quasi-static process is the process where all states at all points are equilibrium states. To obtain such condition, people usually make it very slow. Why? It takes time for the system to reach the equilibrium state B after it changes from state A. The slower you make it, the longer the system remains in state B before it leaves state B, and when it's very slow, you may approximately consider the system as being in state B all the time after changing from A and before jumping to another third state.

So say it takes time T (0.01s, 0.0001s, or even 10s!) for the system to jump from A to B. If you keep it at state B in 1000T, you obtain the quasi-static process. In real life, T is definite; T is not infinitesimal. So strictly speaking, it cannot be quasi-static all the time as you said. It's only approximately is, as Wiki says.

In my opinion, quasi-static process is rather theoretical - an ideal process. So with the understanding I show you above, we can interpolate that theoretically, when T becomes very very small, or infinitesimal (which also means it cannot be measured!) so that the period of jumping from state A to B no longer matters, there is a quasi-static process. That's how practice and theory intersect.

Therefore, your example about cutting the rod/rope/etc shows no paradox. It is an ideal example, where we can cut it to infinite number of infinitesimal pieces. In reality, we simply can't, as molecular scale is our limit.

 

[mikelepore]

The reason thay say to perform a process slowly is to make turbulence negligible. Turbulence is nonconservative like friction.

 

[Gordianus]

The quasistatic process is merely a mathematical limit. It´s easy to see it´s impossible to go from A to B while being always in equilibrium. No real physical process can ever be quasistatic.
So, why do we use such a notion? Firstly we need it to compute easily some magnitudes and to approach the also impossible reversible process.