# HW6 - 14:440:407 Section 02 Fall 2010 SOLUTION OF HOMEWORK...

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Unformatted text preview: 14:440:407 Section 02 Fall 2010 SOLUTION OF HOMEWORK 06 Question 9.1 Consider the sugarwater phase diagram of Figure 9.1. (a) How much sugar will dissolve in 1500 g water at 90 C (194 F)? (b) If the saturated liquid solution in part (a) is cooled to 20 C (68 F), some of the sugar will precipitate out as a solid. What will be the composition of the saturated liquid solution (in wt% sugar) at 20 C? (c) How much of the solid sugar will come out of solution upon cooling to 20 C? Solution (a) We are asked to determine how much sugar will dissolve in 1000 g of water at 90 C. From the solubility limit curve in Figure 9.1, at 90 C the maximum concentration of sugar in the syrup is about 77 wt%. It is now possible to calculate the mass of sugar using Equation 4.3 as C sugar (wt%) = m sugar m sugar + m water 100 77 wt% = m sugar m sugar + 1500 g 100 Solving for m sugar yields m sugar = 5022 g (b) Again using this same plot, at 20 C the solubility limit (or the concentration of the saturated solution) is about 64 wt% sugar. (c) The mass of sugar in this saturated solution at 20 C ( m' sugar ) may also be calculated using Equation 4.3 as follows: 64 wt% = m' sugar m' sugar + 1500 g 100 which yields a value for m' sugar of 2667 g. Subtracting the latter from the former of these sugar concentrations yields the amount of sugar that precipitated out of the solution upon cooling m&amp;quot; sugar ; that is m&amp;quot; sugar = m sugar m sugar = 5022 g 2667 g = 2355 g Question 9.3 Cite three variables that determine the microstructure of an alloy. Solution Three variables that determine the microstructure of an alloy are (1) the alloying elements present, (2) the concentrations of these alloying elements, and (3) the heat treatment of the alloy. Question 9.4 What thermodynamic condition must be met for a state of equilibrium to exist? Solution In order for a system to exist in a state of equilibrium the free energy must be a minimum for some specified combination of temperature, pressure, and composition. Question 9.5 Consider a specimen of ice that is at 2 10 C and 1 atm pressure. Using Figure 9.2, the pressure temperature phase diagram for H 2 O, determine the pressure to which the specimen must be raised or lowered to cause it (a) to melt, and (b) to sublime. Solution The figure below shows the pressure-temperature phase diagram for H 2 O, Figure 10.2; a vertical line has been constructed at -10 C, and the location on this line at 1 atm pressure (point B ) is also noted. (a) Melting occurs, (by changing pressure) as, moving vertically (upward) at this temperature, we cross the Ice-Liquid phase boundary. This occurs at approximately 570 atm; thus, the pressure of the specimen must be raised from 1 to 570 atm. (b) In order to determine the pressure at which sublimation occurs at this temperature, we move vertically downward from 1 atm until we cross the Ice-Vapor phase boundary. This intersection occurs at approximately 0.0023 atm. 0....
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HW6 - 14:440:407 Section 02 Fall 2010 SOLUTION OF HOMEWORK...

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