Problem 1 [40 points]: A thermal gravimetric analyzer (TGA) is a common instrument used in materials science laboratories. In this instrument, a sample is placed on a balance that is suspended inside of a ceramic furnace. The sample can then be heated to a desired temperature under a controlled atmosphere while the mass change of the sample is measured. The sample pan in the TGA is contained within a porous ceramic furnace. The TGA has recently been used to study the sorption and desorption of water from a new material. Unfortunately, the TGA was exposed to a saturated water vapor stream, and water condensed within the porous ceramic wall of the furnace. The TGA will not operate correctly while it is water-logged. You decide to dry the TGA by flowing N2 through the furnace; however, you do not have a water vapor sensor handy, and thus you are not sure how long it will take for the furnace to dry completely. You decide to estimate the drying time for this piece of equipment using some mass transfer approximations. You find the following information: 1. Ceramic properties: Pore size of ceramic (diameter) = 100 nm, porosity = 40%, tortuosity = 2, density of porous ceramic 2.5 g/cm 2. Dimensions of ceramic furnace (Figure 1): a. Outer diameter: 5.0 cm, inner diameter: 2.5 cm, height: 6 cm 3. Water sorption isotherm in the ceramic (Figure 2) 4. Correlation for boundary layer thickness and velocity (Figure 3) a. 8[m] = 5.1x10-5 1 UN2[m/s]' which is approximately valid for all temperatures in this situation: To dry the TGA, you will flow N2 gas at 1 atm through the furnace and heat it. However, one complication exists: if the water content in the furnace is above 0.21 g20/gceramic at temperatures above 100C, the furnace will crack. Hint for this problem: think about the coordinate system carefully to avoid making this problem more difficult than it already is!