6.20. If placed in very smooth, clean containers, many liquids can be supercooled to temperatures below their melting points without freezing, such that they remain in the liquid state. If left long enough, these systems will eventually attain equilib- rium by spontaneously freezing. However, in the absence of nucleation sites like dirt or imperfections in the walls of the container, the time required for freezing can be long enough to permit meaningful investigations of the supercooled state. Consider the spontaneous freezing of supercooled liquid water. For this prob lem you will need the following data taken at atmospheric pressure: cp 38 J/K mol for ice (at 0 °C, but relatively constant over a small T range); Cp-75 J/K mol for liquid water (at 0 °C, but relatively constant); and Δhm-6, 026 J/mol for liquid- ice phase equilibrium at 0 °C. Here Ax indicates iquid Xcrystal for any property x Recall that E + PV, h = H/N, and Cp = (ah/01),-7(os/OT)P, and that h and s are state functions (a) In an isolated system, when freezing finally occurs, does the entropy increase or decrease? What does this imply in terms of the relative numbers of micro- states before and after freezing? Is "disorder" a useful qualitative description of entropy here? (b) If freezing happens fast enough, to a good approximation the process can be considered adiabatic. If the entire process also occurs at constant pressure, how that freezing is a constant-enthalpy (isenthalpic) process (C) If one mole of supercooled water is initially at -10 °C (the temperature of a typical household freezer), what fraction freezes in an adiabatic process as it comes to equilibrium? Compute the net entropy change associated with this event. Note that this is not a quasi-static process. (d) Consider instead the case when the freezing happens at constant T and P. Under these conditions, explain why the expression Δ:-Δh/T is valid when liquid water freezes at its melting point, but not when supercooled liquid water freezes. (e) Compute ASwater, ASsurw and ASworld when one mole of supercooled liquid ater spontaneously freezes at -10 °C (e.g, in the freezer). Assume that the surroundings act as a bath