EML4930/5930 Ceramic Processing - Spring 1998 - Exam Problem #5

Here is the revised problem #5 for your exam. Please use the figure from the original problem.

5)

Density, rho, is defined as mass/volume. In ceramic processing it is desirable to measure the density of objects after sintering. For a cube, density determination is relatively simple: the volume is determined by measuring the length of a side and cubing that dimension, and the mass is determined by weighing. But in every-day life, very few objects are cubes, and it is difficult to measure the true volume of irregularly shaped objects. This challenge resulted in the development of another density measurement technique that is based on liquid displacement, the "Archimedes Method." In the Archimedes method, an object is weighed dry, wdry, and then the object is weighed while suspended in a liquid of known density wsus, shown schematically below. (not shown here, but in original problem) If the following values are known, rhoth - theoretical density of the solid rholiq - density of the liquid wdry - dry weight of the solid wsus - weight of the solid when suspended in the liquid a) derive an equation for the actual density rhoactual, of the irregularly shaped object, in terms of rhoth, rholiq, wdry, and wsus. Considering that the actual density differs from the theoretical density because of porosity, b) derive an equation for the volume percent porosity ( %por = [Vpores / Vtotal] * 100 ), in the solid object in terms of rhoactual, rhoth, rholiq, wdry, and wsus. Please remember that mass and weight are not the same; weight is the force exerted by an object due to acceleration, or, depending to the weighing device, the apparent force exerted by an object. Also, for the sake of this derivation, you may assume that the pores have a finite volume, but a mass of zero.