3.7 Time for a droplet to evaporate. A droplet of pure A of initial radius R is suspended in a large body of motionless gas B. The concentration of A in the gas phase is xAK at r=R and zero at an infinite distance from the droplet. (a) Assuming that R is constant, show that at steady state R2NArR=1xACASr2drdxA where NArlr=R is the molar flux in the r direction at the droplet surface, c is the total molar concentration in the gas phase, and DAB is the diffusivity in the gas phase. Assume constant temperature and pressure throughout. Show that integration of Eq. 19B.7-1 from the droplet surface to infinity gives RNArYRR=CYADln(1xAB) (b) We now let the droplet radius R be a function of time, and treat the problem as a quasi-steady one. Then the rate of decrease of moles of A within the drop can be equated to the instantaneous rate of loss of mass across the liquid-gas interface dtd(34R3CA(L))=4R2NAlr=R=4RcPABln(1xAE) where CA(t) is the molar density of pure liquid A. Show that when this equation is integrated from t=0 to t=t0 (the time for complete evaporation of the droplet), one gets t0=2cDABln[1/(1xAB)]cAdtR2 Does this result look physically reasonable