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Re: [Phys-l] T dS versus dQ



Abstract
This paper focuses on the determination of the final equilibrium state when two ideal gases, isolated from the exterior and starting from preset initial conditions, interact with each other through a piston. Depending on the piston properties, different processes take place and also different sets of equilibrium conditions must be satisfied. Three cases are analysed, namely, when (case 1) the piston is a heat conductor and free to move, (case 2) the piston allows heat conduction but its position is fixed, and (case 3) the piston is free to move but it is adiabatic (so no heat can be exchanged). Cases 1 and 2 have straightforward solutions, but it is shown that case 3 leads to an undeterminable final state. Even though this last situation seems to be strange and difficult, mechanical and thermodynamical analyses are performed. It is shown that the determinability of the final state depends on whether friction is considered or not. Carried out numerically, both analyses provide consistent results and not only do they enable an interesting and useful discussion regarding the concepts of energy, heat, work and entropy, but they also reinforce some ideas which were recently published.


Thermodynamical interactions: subtleties of heat and work concepts
Joaquim Anacleto1,2 and Joaquim Alberto C Anacleto3
1 Departamento de F ́ısica, Universidade de Tra ́s-os-Montes e Alto Douro, Apartado 1013, P-5001-801 Vila Real, Portugal 2 CLOQ-IFIMUP, Departamento de F ́ısica, Faculdade de Cieˆncias da Universidade do Porto, R. Campo Alegre, 687, P-4169-007 Porto, Portugal 3 Departamento de Informa ́tica, Universidade do Minho, Campus de Gualtar, P-4710-057 Braga, Portugal
E-mail: anacleto@utad.pt and a49313@alunos.uminho.pt
Received 13 January 2008, in final form 2 March 2008 Published 25 April 2008 Online at stacks.iop.org/EJP/29/555


bc searching for thermo (emphasis on entropy) instructional lab. expts. for HS.


On 2010, Jan 17, , at 17:10, John Mallinckrodt wrote:


Well ... I fear that much of the confusion in this thread is the
result of differing hidden assumptions about what is given so let's
try to be very specific. First, a few facts:

1. For a given gas at thermal equilibrium, both the energy and the
entropy depend only on the temperature and the volume and, for a
given volume, both the energy and the entropy increase monotonically
with temperature.

2. All of the above is also true for an ideal gas with the slight
simplification that the energy does *not* depend on the volume.


Now some cases. In each, I 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.)


CASE 2: The energy input is specified:

1. We know the work done. (Because the energy input was entirely the
result of work.)

2. We don't know the final temperature. (Because we don't know the
final volume.)

3. We don't know the final entropy. (Because we don't know the final
temperature OR the final volume.)

4. We don't know if stirring occurred. (Because we don't know if the
entropy increased.)


CASE 3: The energy input is specified and the gas is ideal:

1. We know the work done. (Because the energy input was entirely the
result of work.)

2. We know the final temperature. (Because we know the final energy.)

3. We don't know the final entropy. (Because we don't know the final
volume.)

4. We don't know if stirring occurred. (Because we don't know if the
entropy increased.)


CASE 4: The energy input and the final volume are specified.

1. We know the work done. (Because the energy input was entirely the
result of work.)

2. We know the final temperature. (Because we know the final energy
and the final volume.)

3. We know the final entropy. (Because we know the final temperature
and the final volume.)

4. We know if stirring has occurred. (Because we know if the entropy
increased.)

5. We know if the problem specification was unphysical. (Because it
is possible to specify an energy input and final volume that result
in a final entropy that is less than the original entropy and *that*
is physically impossible.)

John Mallinckrodt
Cal Poly Pomona
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