Answer Happy

Continue the analysis of Figure 6.4a: a. Now we unclamp the piston, let it slide freely to a nearby position L - 5, clamp it there, and again let the system come to equilibrium. Here is much smaller than L. Find the difference between the entropy of the new state and that of the old one. b. Suppose we unclamp the piston and let it go where it likes. Its position will then wander thermally, but it's most likely to be found in a certain position Leq. Find this position.
b a SO TE w w T L- Figure 6.4: (Schematics.) Compression of gas by a spring. The direction of increasing d is to the left. (a) Thermally solated system. (b) Subsystem in contact with a heat reservoir, at temperature T. The slab on the bottom of (b) conducts beat, whereas the walls around the box in both panels (hatched) are thermally insulating. In each case the chamber on the right (with the spring) contains no gas; only the spring opposes gas pressure from the left side.