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In lecture, Lavelle said to ignore the vertical brown line. I think it was drawn to compare the irreversible and reversible reactions. But, the external pressure was always constant, it didn't drop down all of a sudden.
If you look on page 275 of the textbook, there is an example problem that shows that the pressure did drop by cooling. However, this takes place before any of the expansion work is actually done, so it is a vertical line. This line could have just as easily not been there, but it is just trying to show that w=pΔv=0 because Δv=0. Then the external pressure stays constant which is why it remains a horizontal line as the volume increases.
The vertical brown line just shows that before the expansion, the external pressure was lowered to a certain amount, then the horizontal line afterward represents that the external pressure stayed constant at that amount.
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