As an example of the evolution of an isolated system toward a state of maximum entropy as one or…

As an example of the evolution of an isolated system toward
a state of maximum entropy as one or more internal constraints are removed,
consider the quantity of ideal gas (m, R, cv) trapped in the piston
and cylinder chamber shown in Fig. P2.6a. The initial volume is V1;
the initial pressure P1 is greater than the pressure that would be
necessary to

support the piston (mass M, area A); therefore, in the
initial state, the piston is held in place with a pin. The space V2 _
V1 located above the piston is evacuated.

The pin is removed, the piston rises, and enough time passes
until a new
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As an example of the evolution of an isolated system toward
a state of maximum entropy as one or more internal constraints are removed,
consider the quantity of ideal gas (m, R, cv) trapped in the piston
and cylinder chamber shown in Fig. P2.6a. The initial volume is V1;
the initial pressure P1 is greater than the pressure that would be
necessary to

support the piston (mass M, area A); therefore, in the
initial state, the piston is held in place with a pin. The space V2 _
V1 located above the piston is evacuated.

The pin is removed, the piston rises, and enough time passes
until a new equilibrium state is reached. Assuming that the piston comes to
rest against the top wall of the cavity, determine the critical piston mass
that differentiates between the final states shown in Figs. P2.6b and c. First,
note that the “system” that is “isolated” has two parts, the gas m and the
piston M. (What are the energy interactions experienced by this system during
the expansion?) In case (b), determine analytically the final temperature T2
(note that V2 is given). In case (c), determine analytically the
final volume V3. Show analytically that in both cases the entropy of
the system increases.

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