A piston, initially completely filled with water vapor, compresses the gas until it is completely liquid (connecting the

[answerhappygod]

A Piston Initially Completely Filled With Water Vapor Compresses The Gas Until It Is Completely Liquid Connecting The 1 (170.69 KiB) Viewed 60 times

A piston, initially completely filled with water vapor, compresses the gas until it is completely liquid (connecting the marked positions in Fig. 1). The piston is held at temperature T = 550K at all times. 2.0 x 108 1.5x 108 Pressure (dynes/cm2) 1.0 x 108 5.0 x 107 0 50 100 150 200 250 300 Volume per mole (cm^3) Fig. 1 Pressure vs. volume for the van der Waals model applied to one mole of H20 at T = 550K. The red line shows the vapor pressure P, at this temperature. (a) Draw the path on Fig. 1 taken if the piston moves slowly enough that the system remains in thermal equilibrium at all times. (b) Sketch a path on Fig. 1 taken if the piston moves fast enough so that the pressure rises past the vapor pressure (say, to 1.2 x 108 dynes/cm²) before a liquid water drop nucleates, but slowly enough so that the subsequent condensation of vapor into the water stays in equilibrium.
Figure 2 shows the chemical potential for the van der Waals model as a function of density at this same temperature. Remember that the Gibbs free energy is un, so this is also the Gibbs free energy per molecule. Note that the van der Waals solution assumes that the system is filled with molecules at a uniform density p, not a mixture of liquid and gas.
-9.00 -9.02 -9.04 -9.06 Chemical potential (10^-13 erg/molecule) -9.08 -9.10 -9.12 -9.14 0.000 0.005 0.010 0.015 0.020 0.025 0.030 Density (moles/cm^3) Fig. 2 Chemical potential u vs. density p for the van der Waals model for H20 at T = 550K. (c) Sketch on a copy of Fig. 2 the free energy one would obtain by allowing for the separation of the water into coexisting liquid and gas. (Ignore the small contribution of surface tension.) If a system can be broken up into two weakly interacting subsystems, then the minimum free energy for the system in the limit of infinite size must be convex (see note 4 on page 322). (d) In your solution to part (c), what are the two weakly interacting subsystems? Why did we need to take the limit of infinite size to ignore surface tension? Is your answer convex?