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

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To calculate entropy change for non-isothermal points on a PV diagram, one can design a reversible isothermal process connecting the initial and final states. This method allows for the calculation of ΔS, which remains valid regardless of the actual process being non-isothermal or irreversible. The initial and final temperatures may differ, but the chosen reversible path simplifies heat flow calculations. By integrating dq/T along this path, the change in entropy can be accurately determined. Thus, the entropy change depends solely on the initial and final states, not the specific path taken.
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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.
 
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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