Adrop of liquid a of radius r1 is suspended in a stream of gas b. there is a spherical stagnant gas film of radius r2 surrounding the droplet. the concentration of a in the gas phase is xa1 at r=r1 and xa2 at the outer edge of the film, r=r2.a) integrate the shell balance to derive the expression for the mole fraction of a in the stagnant film. b) derive an expression for the flux of a at the gas-liquid interface (r=r1).

Simon is writing a story about an astronaut whose spacecraft has been boarded by space pirates. the astronaut has her lucky penny in her hand behind her back as the space pirates break into the control room. she has just locked the controls so that the ship is accelerating in the direction of the control room’s ceiling. simon wants the astronaut to use the penny to hit a button on the control panel to turn off the lights and escape. the button is located a short distance behind and below the astronaut’s hands. how should simon use the theory of relativity to describe what the astronaut must do in order to hit the button?