1) You are walking through the school gymnasium and you accidently lose your Helium filled rubber balloon which floats to the ceiling. Willie, the school's groundkeeper offers to get his ladder to retrieve the balloon. You tell him not worry and to just wait as it will come down on its own, because of diffusion! The balloon is initially inflated to a radius of 6 inches (assume a sphere). The balloon's empty mass is 10 g. The density of the rubber is 0.8 g/cm'. a) List and explain (in one bullet each) at least 3 assumptions that you are making about the balloon, the gas, the environment, or the diffusion process in order to set up your solution (15 pts) b) What is the approximate thickness of the balloon wall? (15 pts) c) Assuming the contents of the balloon are purely helium @p-1 atm, T=300 K, how much less mass is in the He balloon than in an equivalent balloon full of air? What is the amount of lift generated by the He balloon? (15 pts) d) Assume that D=3.00E-8 kg/m's for the He through the balloon material and assume the pressure inside the balloon does not change much. Calculate the time required for the balloon to start to sink. Willie complains that there will be a dance in the gym in 4 days. Will the balloon drop before then? (30 pts) e) If the balloon will not drop before the dance, Willie decides he will crank up the temperature in the gym to speed up the process. At what temperature does the gym's thermostat have to be set for the balloon to drop before the dance? If the balloon was already going to drop in time, what is the lowest the gym temperature can be set to and still have the balloon drop in 4 days? (25 pts) 1) You are walking through the school gymnasium and you accidently lose your Helium filled rubber balloon which floats to the ceiling. Willie, the school's groundkeeper offers to get his ladder to retrieve the balloon. You tell him not worry and to just wait as it will come down on its own, because of diffusion! The balloon is initially inflated to a radius of 6 inches (assume a sphere). The balloon's empty mass is 10 g. The density of the rubber is 0.8 g/cm'. a) List and explain (in one bullet each) at least 3 assumptions that you are making about the balloon, the gas, the environment, or the diffusion process in order to set up your solution (15 pts) b) What is the approximate thickness of the balloon wall? (15 pts) c) Assuming the contents of the balloon are purely helium @p-1 atm, T=300 K, how much less mass is in the He balloon than in an equivalent balloon full of air? What is the amount of lift generated by the He balloon? (15 pts) d) Assume that D=3.00E-8 kg/m's for the He through the balloon material and assume the pressure inside the balloon does not change much. Calculate the time required for the balloon to start to sink. Willie complains that there will be a dance in the gym in 4 days. Will the balloon drop before then? (30 pts) e) If the balloon will not drop before the dance, Willie decides he will crank up the temperature in the gym to speed up the process. At what temperature does the gym's thermostat have to be set for the balloon to drop before the dance? If the balloon was already going to drop in time, what is the lowest the gym temperature can be set to and still have the balloon drop in 4 days? (25 pts)