How Do We Calculate Entropy Change for Non-Isothermal Points on a PV Diagram?

In summary, to find the change in entropy for two points on a P V diagram which are not an isotherm, you can design an isothermal reversible process between the two points and calculate its ΔS. The temperature at the initial and final states may not be the same, but any reversible path can be used to determine the heat flow and calculate the integral of dq/T, giving the change in entropy.
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how do we find change in entropy for two points on a P V diagram which are not an isotherm
 
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Since the change in entropy of the system only depends on the initial and final states of the system, you can design an isothermal reversible process which goes from the intial point to the final point indicated by the diagram and easily calculate its ΔS. It will be the same even if the actual process you are studying is not isothermal or reversible.
 
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MexChemE said:
Since the change in entropy of the system only depends on the initial and final states of the system, you can design an isothermal reversible process which goes from the intial point to the final point indicated by the diagram and easily calculate its ΔS. It will be the same even if the actual process you are studying is not isothermal or reversible.
The temperature at the initial state may not be the same as the temperature in the final state. So the path may not be totally isothermal. But you have the right idea.

The OP needs to "dream up" a reversible path between the initial and final states (any reversible path will suffice) for which the heat flows are easy to determine, and then calculate the integral of dq/T for that reversible path. That will give the change in entropy.

Chet
 
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FAQ: How Do We Calculate Entropy Change for Non-Isothermal Points on a PV Diagram?

1. What is entropy?

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it is often described as the amount of energy that is unavailable for work in a closed system.

2. How do you calculate change in entropy?

The change in entropy (ΔS) can be calculated using the equation ΔS = Q/T, where Q is the heat transferred and T is the temperature in Kelvin.

3. What factors affect the change in entropy?

The change in entropy is affected by the amount of heat transferred, the temperature, and the system's physical state. It also depends on the type of process (e.g. isothermal, adiabatic, reversible) and the number of particles in the system.

4. Why is the change in entropy important?

The change in entropy is important because it helps us understand the direction and efficiency of processes. In any spontaneous process, the total entropy of the system and its surroundings increases.

5. How does entropy relate to the second law of thermodynamics?

The second law of thermodynamics states that the total entropy of a closed system always increases over time. This means that in any spontaneous process, the total entropy of the system and its surroundings will increase, or at least remain constant. Entropy provides a quantitative measure of this law.

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