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Re: [Phys-l] T dS versus dQ

A well insulated cylinder with a low thermal mass and conductivity piston. The top of the piston's con rod, instead of a handle, has a weight cup. (included P and T sensors)

Trial A; continuously and slowly add small weights 'till the V is, say, 1/10 the original.

Trial B dump the weights in all at once (a single weight = in mass to the above ones)

discussion: P and T and from the discussion S will differ, but the work mgh will be the same.

No, mgh is not the same in the two cases. In trial B you slid the entire weight m off a shelf that is at the starting height of the piston. (Say it's 50 cm above the bottom of the cylinder.) In trial A, you move small weights off a succession of shelves of *gradually decreasing heights* so that each weight is slid off onto the piston at the instant that they are at the same height as each other. Ergo, less work was done in trial B.

A full analysis of this kind of problem is in the following brief paper of mine and addresses many of the points discussed in this thread: