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The following figure describes the particle size distribution in a dispersion of copper oxide particles in water: (a) (15 points) Calculate the number average diameter, surface area average diameter and volume average diameter of the particles. (b) (15 points) Three students used different techniques to measure the average diameter of the particles. The first student used a BET gas adsorption test. The second student used a microscope. The third student used light scattering. Which student obtained the smallest particle diameter? Which student obtained the largest particle diameter? Which student obtained a particle diameter that was intermediate to the smallest and largest calculated particle diameters? (c) (Graduate Students (15 Points); Undergraduates, Extra Credit) After milling the particles, the particle distribution changed as shown below. After milling, should the magnitude of the Gibbs free energy of the particle system increase or decrease? Why? Calculate the Gibbs free energy change (in SI units) between the milled and unmilled particles. Give sufficient mathematical description to support your conclusions and calculations (i.e., show your work). The surface energy, , of copper oxide is 1200mJ/m2(1.2J/m2). The following figure describes the particle size distribution in a dispersion of copper oxide particles in water: (a) (15 points) Calculate the number average diameter, surface area average diameter and volume average diameter of the particles. (b) (15 points) Three students used different techniques to measure the average diameter of the particles. The first student used a BET gas adsorption test. The second student used a microscope. The third student used light scattering. Which student obtained the smallest particle diameter? Which student obtained the largest particle diameter? Which student obtained a particle diameter that was intermediate to the smallest and largest calculated particle diameters? (c) (Graduate Students (15 Points); Undergraduates, Extra Credit) After milling the particles, the particle distribution changed as shown below. After milling, should the magnitude of the Gibbs free energy of the particle system increase or decrease? Why? Calculate the Gibbs free energy change (in SI units) between the milled and unmilled particles. Give sufficient mathematical description to support your conclusions and calculations (i.e., show your work). The surface energy, , of copper oxide is 1200mJ/m2(1.2J/m2)