# Definition of Entropy for Irreversible Processes

• Hummel
In summary, entropy is a measure of the Disorder or Unorderedness of a system. It can only be calculated for equilibrium states.

#### Hummel

What is the definition of entropy of a thermodynamic irreversible process?

In the case of reversible process from initial state 'a' to final state 'b' ,one may define entropy
by

1) Constructing infinitely many reservoirs having temperatures corresponding to the temperature at every point on the P-V diagram of the process from 'a' to 'b'

2) Finding $\frac{dQ}{T}$ at every point
where dQ is the elemental heat transferred at every point,T is the corresponding temperature at the point.
3)Now by linking each reservoir of temperature T to a reservoir at unit absolute thermodynamic temperature by a reversible heat engine.

4) ∴ ,$\frac{dQ}{T}$ = $\frac{Qs}{1}$ = dS

5) Now integrating the entropy of every elemental part on the P-V curve,we get the total change in entropy as
ΔS = $\int^{b}_{a}\frac{dQ}{T}$

(Abs. entropy can be determined using nernst theorem)

Similarly,how can we determine the entropy or change in entropy for a irreversible process.

Gentlemen,i would be happy if we stick to a thermodynamic approach rather than Quantum mechanical approach(of course unless it is necessary)
(My sincere Request:For god's sake, please don't talk about entropy as randomness)

Entropy has meaning only for equilibrium states. If we have some process (does not matter whether it is reversible or not) that takes the system from the state ##A## to state ##B##, the change in entropy is

$$\Delta S = S(B) - S(A).$$

So, we need to know the states A,B and their entropy.

Hummel said:
What is the definition of entropy of a thermodynamic irreversible process?

It's the same as for a reversible process as far as I know. While the entropy of an irreversible process can't be calculated directly, the change in entropy a is state function independent of path, so one should be able calculate $\Delta S$ by approaching the problem as if the process were reversible.

http://www.files.chem.vt.edu/chem-dept/marand/set6.pdf [Broken]

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Jano L. said:
Entropy has meaning only for equilibrium states. If we have some process (does not matter whether it is reversible or not) that takes the system from the state ##A## to state ##B##, the change in entropy is

$$\Delta S = S(B) - S(A).$$

So, we need to know the states A,B and their entropy.

Sir,my question was how do you define entropy for irreversible process?
apart from that,How do you determine S(B) and S(A)?

SW VandeCarr said:
It's the same as for a reversible process as far as I know. While the entropy of an irreversible process can't be calculated directly, the change in entropy a is state function independent of path, so one should be able calculate $\Delta S$ by approaching the problem as if the process were reversible.

http://www.files.chem.vt.edu/chem-dept/marand/set6.pdf [Broken]

I totally appreciate the PDF attachment.
I will get back once i completely go through it and if if we have to iron out any kinks.

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If the initial and final equilibrium states for the irreversible process are well defined, you need to dream up (i.e., conceive of) a reversible process that gets you between these same two equilibrium states, and use that process to calculate the change in entropy.

Chet

## What is entropy?

Entropy is a thermodynamic quantity that measures the disorder or randomness of a system. It is a measure of the number of possible arrangements of a system's particles or energy that are consistent with its macroscopic state.

## How is entropy defined for irreversible processes?

The definition of entropy for irreversible processes is based on the second law of thermodynamics, which states that the total entropy of an isolated system always increases over time. For irreversible processes, the change in entropy is equal to the heat transferred to the system divided by the temperature at which the transfer occurs.

## What is the significance of entropy in thermodynamics?

Entropy is a fundamental concept in thermodynamics and plays a crucial role in understanding the behavior of physical systems. It helps to explain the direction of spontaneous processes, the efficiency of heat engines, and the availability of energy in a system.

## How does entropy relate to disorder and randomness?

Entropy and disorder are closely related, as an increase in entropy is associated with an increase in disorder in a system. The more disordered a system is, the higher its entropy. Randomness also plays a role in entropy, as a system with more possible arrangements of its particles or energy will have a higher entropy.

## Can entropy be reversed?

While entropy can decrease in a local system, the total entropy of an isolated system will always increase over time. This is known as the arrow of time, and it is a fundamental principle in thermodynamics. Therefore, entropy cannot be reversed in an isolated system.