Why Is Reversibility Essential for Using dS=δQ/T?

In summary, the conversation discusses the use of dS=\frac{\delta Q}{T} and \delta Q=TdS in solving thermo problems. It is mentioned that dS is a state variable and its change remains the same regardless of whether the transformation is reversible or not. However, in order to calculate the change in S, it is necessary to integrate along a reversible path. It is also noted that the integral TdS is always less for an irreversible change compared to a reversible one. The speaker also mentions that E. Fermi's book "Thermodynamics" proves this fact, but it is not fully understood. The book is described as being complex and difficult to understand.
  • #1
Proust
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Homework Statement



In my book it says, "only if the transformation is reversible can we use [itex]dS=\frac{\delta Q}{T}[/itex]", but I don't know why? I think even if it's not reversible we also use [itex]\delta Q=TdS[/itex] to solve the thermo problems, don't we?

I'm looking forward to your ideas, thanks.
 
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  • #2
Entropy is a state variable. That means that, no matter how we get from state A to state B, the change in S is the same. Doesn't matter if the change is reversible or not.

The point is that in order to CALCULATE the change in S, you must integrate along a reversible path.

In fact, the integral TdS from state A to B is always less for an irreversible change than for a reversible one. E. Fermi proves this in his Dover book "Thermodynamics' but I never followed the proof. Since the states are undefined for an irreversible change I don't lose too much sleep over it. But Fermi actually invokes that fact later in the book on a different topic.

If you want to get totally snowed, that is the book for you!
 

FAQ: Why Is Reversibility Essential for Using dS=δQ/T?

What is the concept of reversibility in thermodynamics?

Reversibility in thermodynamics refers to a process in which all changes within a system can be reversed by an infinitesimal change in the conditions. This means that the system would return to its original state after the process is reversed, without any loss or gain of energy.

How does entropy play a role in reversible processes?

Entropy is a measure of the disorder or randomness of a system. In reversible processes, the entropy of a closed system remains constant, as the system returns to its original state after the process is reversed. This means that there is no net increase or decrease in the disorder of the system.

Can all processes in nature be considered reversible?

No, not all processes in nature are reversible. In fact, many processes are irreversible due to factors such as friction, heat transfer, and chemical reactions. These processes result in an increase in entropy and a loss of energy, making them irreversible.

What is the relationship between reversible and irreversible processes?

Reversible and irreversible processes are essentially opposite concepts. Reversible processes are ideal and involve no energy loss, while irreversible processes involve energy loss and an increase in entropy. However, reversible processes can serve as a theoretical basis for understanding and approximating real-world irreversible processes.

How is the concept of reversibility applied in real-world systems?

In real-world systems, the concept of reversibility is often used as a theoretical ideal to approximate the behavior of actual processes. Engineers and scientists strive to design processes and systems that are as close to reversible as possible, in order to minimize energy losses and increase efficiency.

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