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These equations find important applications in phase-equilibrium thermodynamics Equations (1190) and (1191) allow direct calculation of the effects of pressure and temperature on the excess Gibbs energy For example, an equimolar mixture of benzene and cyclohexane at 29815 K (25 C) and 1 bar has an excess volume of about 065 cm3 molpl and an excess enthalpy of about 800 J mol-' Thus at these conditions, 065 = 262 x lop5 bar-' [ a ( G z T ) ] T , x = (8314)(29815)

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The most striking observation about these results is that it takes a pressure change of more than 40 bar to have an effect on the excess Gibbs energy equivalent to that of a temperature change of 1 K (1 C) Similar calculations based on Eqs (1193) and (1194) produce similar results This is the reason that for liquids at low pressures the effect of pressure on the excess Gibbs energy and on the activity coefficients is usually neglected Just as the fundamental property relation of Eq (1150) provides complete property information from a canonical equation of state expressing G I R T as a function of T, P , and composition, so the fundamental residual-property relation, Eq (1151) or (1 152), provides complete residual-property information from a P V T equation of state, from P V T data, or from generalized P VT correlations However, for complete property information, one needs in addition to P V T data the ideal-gas-state heat capacities of the species that comprise the system In complete analogy, the fundamental excess-property relation, Eq (1186) or (1 189), provides complete excess-property information, given an equation for GE/RT as a function of its canonical variables, T, P, and composition, However, this formulation represents lesscomplete property information than does the residual-property formulation, because it tells us nothing about the properties of the pure constituent chemical species

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digital or 35mm camera supports very long exposures You can compare techniques and see if the digital way is easier, here s how I did it in college: 1 Set the camera up on a tripod in total darkness and start a long exposure 2 Using a flash, expose the subject (like someone holding a phaser) and the target person The flash does not need to be mounted to the camera you can just take a flash unit and hold it in your hand, flashing the subject once or twice 3 Get behind the subject, and, pointing a flashlight directly at the camera, walk to the target of the phaser blast, trying to keep the flashlight moving in a straight line so it traces what will look like a solid laser beam on the film 4 Outline the target with the flashlight, again pointing it at the camera 5 If you want to make the target look as if he or she is disintegrating, ask the subject to leave the scene and then flash the rear wall once 6 Stop the exposure That s a lot of work, and the results are often hit or miss Against all odds, you can sometimes get a half-decent one

Peculiarities of liquid-mixture behavior are dramatically revealed in the excess properties Those of primary interest are GE, H E , and sE The excess Gibbs energy comes from experiment through reduction of vaportliquid equilibrium data, and H E is determined by mixing experiments (Chap 12) The excess entropy is not measured directly, but is found from

Eq (1183), written:

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Excess properties are often strong functions of temperature, but at normal temperatures are not strongly influenced by pressure Their composition dependence is illustrated in Fig 114 for six binary liquid mixtures at 32315 K (50 C) and approximately atmospheric pressure For consistency with Eq (1183), the product T S E is shown rather than S E itself Although the systems exhibit a diversity of behavior, they have common features: 1 All excess properties become zero as either species approaches purity 2 Although G E VS X I is approximately parabolic in shape, both H~ and T S exhibit indi~ vidualistic composition dependencies 3 When an excess property M E has a single sign (as does G E in all six cases), the extreme value of M E (maximum or minimum) often occurs near the equimolar composition

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