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Re: [Phys-l] T dS versus dQ

Bernard Cleyet wrote:
Is this a "good" experiment:
It is not a good experiment, in one respect.
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.
We may visualize this continuous process approximately, with a series of weights stationed between the starting position of the cup and piston, and its lower final position.
Trial B dump the weights in all at once (a single weight = in mass to the above ones)

We may visualize this discrete process by adding the sum of the weights mentioned in Trial A all at the highest position mentioned in Trial A
discussion: P and T and from the discussion S will differ, but the work mgh will be the same. Is this experiment at least qualitatively possible and instructive?
bc prays he's not all wet here.
I ask you to consider the potential energy contributed in Trial A to the potential energy contributed in Trial B.


No, of course they are not the same.
If the energy contributed in trial A was sufficient to provide the compressed volume desired, where does the EXTRA energy provided in Trial B go?
Into heating the gas, increasing its entropy.
On 2010, Jan 17, , at 17:10, John Mallinckrodt wrote:
...assume a) that the gas is thermally insulated, b) that it starts and ends in thermal equilibrium, and c) that the initial state is given.

CASE 1: An irreversible compression to a given final volume, (i.e. Carl's case):

1. Stirring has occurred and the final entropy is greater than the initial entropy. (Because we are explicitly told that the process is irreversible.)

2. The final energy is greater than it would have been had the process not been irreversible. (Because higher entropy => higher temperature => higher energy for a given volume.)

3. More work was done on the gas than would have been had the process not been irreversible. (Because the extra energy was entirely the result of extra work done.)
Brian W
p.s. I leave aside consideration of the final volume of the gas, when compressed using the Trial B "sudden" method, compared with the final volume achieved using the Trial A "gradual" method.