Gibbs and Diffusion Questions

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1.) (1.5 point) Using the data table below for the following liquids, use the free-volume theory we discussed in class to determine the AG'. Is there any relationship between their molecular structure and interactions and AG'? For generality, you may assume that 8=1. You can also assume an average molecular weight of 200 g/mol, although this may not be reasonable (why?); R134A is tetrafluoroethane. Engine oil Ethylene glycol Refrigerant 134A Water Temp Density Viscosity Density Viscosity Density Viscosity Density Viscosity (K) (kg/m³) (106 (kg/m³) (106 (kg/m²) (106 (kg/m³) (106 Ns/m²) Ns/m2) Ns/m²) Ns/m²) 273 899.1 385 1130.8 6.51 1304.7 277.54 1000 1750 280 895.3 217 1125.8 4.20 1271.4 244.34 1000 1422 290 890.0 99.9 1118.8 2.47 1236.3 215.64 999.0 1080 300 884.1 48.6 1114.4 1.57 1199.3 190.46 997.0 855 310 877.9 25.3 1103.7 1.07 1159.5 168.04 993.1 695 320 871.8 14.1 1096.2 0.757 1116.4 147.78 989.1 577 330 865.8 8.36 1089.5 0.561 1068.8 129.20 984.3 489 2.) (1.5 point) The thermal conductivity of a liquid is more obscure than that of gases. However, we can modify the kinetic theory approximation we derived for the thermal conducted of a gas to apply to liquids. The average velocity of gas and liquid particles can be written in terms of the absolute temperature and mass of the particles and the speed of sound in the material (ca): 8kB7 8C, y = gas mm Cig 8Cv Vliquid = CAL* mCp In a liquid, the heat capacity at constant volume, Cv, is ~3R/Mw, instead of 3R/2Mw for gases. The mean free path is the cube root of the volume per molecule of liquid: Mw As= ONA. A.) Determine an expression for k, the thermal conductivity (W/mK), in terms of Avogadro's number, Boltzmann constant, heat capacities (Cv and CP), density, and speed of sound (cu). B.) Calculate the thermal conductivity for the following liquids (you can assume Cv/Cp~l). C.) Compare these results with the experimental values Liquid Density MW (kg/kmol) Sonic Velocity kexp (W/mK) (kg/m³) ca (m/s) H2O 1000 18 1497.6 0.342 CH3COCH3 790 58 1174 0.105 CH3CH2OH 790 46 1207 0.126 CHCL3 1490 119.35 987 0.083 Hg 13500 200.6 1450 0.377 3.) (0.5 points) If we consider the kinetic theory expressions for the viscosity, thermal conductivity, and diffusivity, we can express them in the following form: u pCv k = 3Dag: JA, = p The product of velocity and mean free path has the dimensions of length2/time, or diffusivity. In the preceding equation, all quantities on the left-hand side represent a diffusivity, specifically the same diffusivity. Comment on what this means for the mechanism whereby mass, energy, and momentum are transported in gas. Would you expect the same type of mechanism to operate in a liquid? In a solid? What would be required for the same mechanism to operate?

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