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Solution 1

# Solution 1 - mse 103 Phase Transformations and Kinetics...

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Unformatted text preview: mse 103 Phase Transformations and Kinetics Spring 2009 University of California Problem set 1 Solution Due: Wednesday, January 28 th , by 11:10am before lecture begins; late homework will not be accepted 1. The schematic below shows a hypothetical P-T diagram for zinc. The diagram has a basic error in its construction. First, identify where the error is, and then provide a concise but complete explanation of why this must be an error. (Note: An explanation that merely says something like “this line should slope the other way” will only receive partial credit; to get full credit you must explain and demonstrate why the line has to slope the other way) (10 points) Given: V solid = 9.16 cm 3 /mole V liquid = 9.94 cm 3 /mole P T s l v Solution: The sign of the slopes is correct, but the relative values of the slopes are not all correct. The construction problem arises near/at the triple point. The slopes of the solid-vapor equilibrium line and the liquid-vapor equilibrium lines are shown as being equal. From the Clapeyron equation , this would require that the ratio of ! S / ! V be the same for the two distinct phase pairs. Under any reasonable circumstance, the volume change is essentially the volume of the gas phase. As seen above, the molar volumes of the solid and liquid are very small in comparison to a typical gas volume. (The triple point temperature and pressure determined later indicate that this is true in the present case as well.) Equality of slope then dictates that the entropy change be the same for the two equilibria, and this in turn requires that the molar entropy of the solid and liquid be equal at the triple point. This is not the case. 2. The vapor pressures of zinc have been written in the form: ln p (atm) = ! 15,780 T ! 0.755ln T + 19.25 ( i ) ln p (atm) = ! 15,250 T ! 1.255ln T + 21.79 ( ii ) One of these expressions gives the equilibrium vapor pressure for pure solid zinc and the other gives the equilibrium vapor pressure for pure liquid zinc. Determine which relationship is which. A lucky guess will earn no credit. There are multiple ways to answer this question. You must provide a clear explanation. ( 10 points ) Solution: As indicated, there are multiple ways in which one could approach this problem. I will provide one solution in detail, and then simply mention other ways in which one could have attacked the problem. The expression for the equilibrium vapor pressure of the solid will define an equilibrium line in a one- component phase diagram. The pressure-temperature relationship appears as the boundary of the fields of stability of the solid and vapor. It is along this line that the chemical potential surfaces of the fields of stability of the solid and vapor....
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Solution 1 - mse 103 Phase Transformations and Kinetics...

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