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rtareen
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- TL;DR Summary
- An example of an irreversible free expansion is given and is related to a reversible isothermal expansion of a gas in a piston-cylinder-reservoir system. The changes in entropy of both systems must be the same as they have the same initial and final states.
Hi all. I am referencing the example given in Halliday and Resnick, Chapter 20, Section 1, Subsection "Change in Entropy". The above picture is graph of the free expansion of a gas into a volume that is double its original volume. I n a free expansion there is no heat transfer, the pressure decreases while the volume increases, and there is no work done. But then they go on to say that this has the same change in entropy as a gas in a piston-cylinder where the some mass is removed from the piston so the that gas expands from the same initial state to the same final state, and heat is added to keep it at the same temperature. Here is the plot of the reversible process:
As we can see the temperature remains constant in this second system. But how does this correspond to a free expansion where the temperature obviously decreases? They are saying the initial and final states are the same for both systems, but I don't see how this can be the case. How can the temperature remain the same in a free expansion? The equation ##\Delta T = \Delta p \Delta V/nR## implies a decrease in temperature.
Also, they say that heat is added to keep the temperature constant, and that’s why the second system gains entropy. But there is no heat transfer in a free expansion, so I’m not understanding the relationship between the two examples. Does this mean that entropy of an irreversible process doesn't depend on heat transfer but the corresponding reversible process does? So then what is entropy really a measure of?