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Topic: Change in Entropy and Entropy as a state function  (Read 516 times)

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Offline Kyriee

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Change in Entropy and Entropy as a state function
« on: December 15, 2019, 09:56:41 AM »
Hi!
I'm studying PChem1 and I'm doing some exercises about change in Entropy.
I cannot understand one basic and fundamental point about entropy: it is a state function and, like all state functions, what matter are the initial and the final states. If this is correct, how is it possible that the variation in entropy is different if I'm talking about, for example, a reversible or an irreversible (against an external pressure different from zero) gas expansion? The fact that the trasformation is reversible or not doesn't change my initial or final states, it only changes the way I arrive to the final state.

Sorry for my bad english and sorry if this is a stupid question, but I'm desperate.

Offline Enthalpy

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Re: Change in Entropy and Entropy as a state function
« Reply #1 on: December 16, 2019, 01:34:13 PM »
Hi Kyriee!

Are the final states really identical? For instance a gas could attain the same final pressure, but with a different temperature and volume, if an expansion is lossy.

Offline Corribus

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Re: Change in Entropy and Entropy as a state function
« Reply #2 on: December 16, 2019, 01:37:56 PM »
Are the final states really identical?
No, which resolves the apparent contradiction.
What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?  - Richard P. Feynman

Offline Kyriee

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Re: Change in Entropy and Entropy as a state function
« Reply #3 on: December 17, 2019, 02:07:28 AM »
Why aren't they?
Let's suppose an isothermic expansion of an ideal gas. The states (Pi,Vi), (Pf, Vf) are the same if the expansion is reversible or irreversible; what does change is the work done. Does the variation in entropy have something to do with this work?

I repeat, sorry if these are basic questions, but I really can't understand.

Offline Corribus

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Re: Change in Entropy and Entropy as a state function
« Reply #4 on: December 17, 2019, 10:00:38 AM »
For example. In an irreversible process there may be heat loss from the system. Therefore the final state of the system that undergoes an irreversible process is different from the final state of the system that undergoes a reversible process, in which no heat is lost. The environment is different in the two processes. Heat, in other words, is not a state function, and the "system" is everything, including the environment. The entropy change during the two processes is not the same, because the final states (which includes the environment) is not the same.
What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?  - Richard P. Feynman

Offline Kyriee

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Re: Change in Entropy and Entropy as a state function
« Reply #5 on: December 17, 2019, 12:06:54 PM »
Let's take an isothermic expansion of an ideal gas as example.
In a reversible process, the work done by the system is w=nrT*ln(Vf/Vi). Being the process isothermic, q(absorbed)=w(done), since the difference in energy is 0.
In a reversible process, the work is w=p(Vf-Vi), which is equal to q, since it is also isothermic.
In both cases, the heat absorbed by the enviroment is equal to the heat released by the system. So, in the case which T(enviroment)=T(system), the variation in entropy of the universe is zero? Regardless of the reversible/irreversible nature of the transformation?

If not, can you suggest me a book where to study or understand this basic concept? I've tried Atkins, McQuarrie, youtube videos, but I'm still stuck.

Offline Enthalpy

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Re: Change in Entropy and Entropy as a state function
« Reply #6 on: December 17, 2019, 12:59:20 PM »
Many situations imagined in thermodynamics books and courses aren't completely described. They often forget some elements that provide or absorb work, so for instance "working against the external pressure" isn't all. Missing energy amounts, and resulting logical contradictions, often come from these omitted elements.

And for reversibility, one also must consider other bodies than the gas, vapour... whose behaviour is described. If other components provide heat from a higher temperature or regain it at a lower temperature, a transformation isn't reversible, the entropy increases, but you may not see it at the mentioned body.

In the last example you describe, the pressure of the ideal gas varies (or nothing would happen) so it's not always equal to the outside pressure. A constant outside pressure absorbs work in this process, but more elements are needed to absorb the difference of pressure between the expanded gas and the outer fluid. It can be a piston for instance. This piston absorbs work. Maybe the work converts immediately to kinetic energy, but it's work.

Sidenotes:
"Energy" isn't accurate enough for thermodynamics. You probably meant the internal energy. There are a dozen more.
If the gas expands at constant temperature, it absorbs heat that is lost by something else.

Offline Kyriee

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Re: Change in Entropy and Entropy as a state function
« Reply #7 on: December 17, 2019, 01:48:15 PM »
I'm really sorry but I don't get it, even if your explanations are good and rigorous.
Thank you very much anyways.

Can you please suggest me some sources that you find useful to resolve this issue?

Offline Enthalpy

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Re: Change in Entropy and Entropy as a state function
« Reply #8 on: December 18, 2019, 12:21:16 PM »
I know no clear book for thermodynamics, and I regret it. Yves Rocard maybe, but it's in French.

About the last case you proposed: the hypotheses you make are not consistent, so the reasoning can't bring good conclusions.

The expansion at constant temperature needs a variable pressure. But this expansion shall work against a constant outer pressure. This needs an extra element between the inner and outer fluids, like a piston, which takes or gives work but is absent from your description.

Offline Kyriee

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Re: Change in Entropy and Entropy as a state function
« Reply #9 on: December 20, 2019, 08:31:27 AM »
Thank you!

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