SolutionР?(a) This problem asks that we derive Equation 4.7a. To begin, C1 is defined according to Equation 4.3 asРor, equivalentlyРwhere the primed m's indicate masses in grams. From Equation 4.4 we may writeРAnd, substitution into the C1 expression aboveРFrom Equation 4.5 it is the case thatРAnd substitution of these expressions into the above equation leads toРwhich is just Equation 4.7a.Р?(b) This problem asks that we derive Equation 4.9a. To begin, is defined as the mass ponent 1 per unit volume of alloy, orРIf we assume that the total alloy volume V is equal to the sum of the volumes of the two constituents--i.e., V = V1 + V2--thenРFurthermore, the volume of each constituent is related to its density and mass asРThis leads to РFrom Equation 4.3, m1 and m2 may be expressed as follows:
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