Why is entropy a state variable even for irreversible path?

In summary, the concept of entropy S is a state variable or state function that can be calculated by integrating dS = dQ/T, provided that the process path is reversible. However, this path-independency breaks down when irreversible processes are involved. As a result, S can only be considered a state variable when there are no irreversible processes. To determine the change in entropy for a system that has experienced an irreversible process, one can follow a cookbook recipe provided in a link.
  • #1
goodphy
216
8
Hello.

The entropy S is a state variable or state function as the integral of dS = dQ/T is a path-independent, provided that the path is reversible process path. However, such a path-independency of the integral breaks down when the path includes irreversible process. So, I guess we can only say that S is a state variable only if there is no irreversible process, but the textbook said S is the state variable no matter the process includes irreversible process or not.

Well..if there is at least one irreversible process path along which the path-independency doesn't hold, how can I justify that S is a state variable?

I would like to get your help to clarify this confusion.
 
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  • #2
Suppose you had an irreversible process path that took your system from thermodynamic equilibrium state A to thermodynamic equilibrium state B. How would you determine the change in entropy for your system?
 

1. Why is entropy considered a state variable?

Entropy is considered a state variable because it only depends on the current state of the system, regardless of how that state was reached. This means that the value of entropy will remain the same even if the process used to reach that state is reversible or irreversible.

2. How is entropy different from other thermodynamic properties?

Unlike other thermodynamic properties, such as temperature or pressure, entropy is not affected by the path taken to reach a particular state. This is because entropy is a measure of the disorder or randomness of a system, which is independent of the specific process used to reach that state.

3. Why does entropy increase in irreversible processes?

In irreversible processes, there is an inevitable loss of usable energy due to dissipation and irreversibility. This increase in disorder leads to an increase in the overall entropy of the system. In contrast, reversible processes do not result in any net change in entropy.

4. Can entropy be decreased in a system?

While it is possible to decrease the entropy of a system, it requires an input of external energy or work. This is because any decrease in entropy must be offset by an equal or greater increase in the entropy of the surroundings, in accordance with the Second Law of Thermodynamics.

5. Is entropy conserved in a closed system?

No, entropy is not conserved in a closed system. The Second Law of Thermodynamics states that the total entropy of a closed system will always increase over time. This means that, while the entropy of individual components may decrease, the overall entropy of the system will continue to increase.

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