Problem 1 A spherical ball of solid naphthalene with initial radius Ro is suspended at time t = 0 from the ceiling in the middle of a very large room, using a thin thread. Naphthalene undergoes sublimation to gaseous form and diffuses out into the surroundings. Because the room is very large compared to the diameter of the naphthalene ball, we can ignore the effects of the walls as a first approximation. The vapor pressure of naphthalene at the temperature of the room is psat, which is very low compared to atmospheric pressure. The solid density of naphthalene is Ps, and its molecular weight is Mw. Stating all assumptions that you need to make and mentioning when each assumption would be valid, answer the following: a) First focus on the naphthalene ball itself, and ignore that it is placed in a large room. Assuming pseudo-steady state and writing a differential mass balance, find an expression for the rate of naphthalene release into the atmosphere. b) What condition must be satisfied for the pseudo-steady state analysis of part a to be valid? Your answer must be in terms of known parameters in the problem statement. c) Now turn your attention to the larger problem (the room). Derive an expression for the concentration of naphthalene in the room as a function of spatial location and time. Note that, when taking the large room to be your mass transfer zone, the naphthalene ball is extremely small. Your expression must be in terms of known parameters in the problem statement. d) Approximately how long will it take for the naphthalene ball to disappear? Obviously, we are looking for an expression here, not a number