Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN: 9781259696527
Author: J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher: McGraw-Hill Education
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![19B.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
infinite distance from the droplet.
gas phase is x,
AR at r = R and zero at an
(a) Assuming that R is constant, show that at steady state
AB 2 dx
dr
R²NArlr=R
(19B.7-1)
XA
where Nl-R is the molar flux in the r direction at the droplet surface, c is the total molar
concentration in the gas phase, and DAR 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
АВ
RNArlr=R =
= -cD
АВ
In(1 - XAR)
(19B.7-2)
(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
d
-TR°C) = 47R°N olar = -4rRcDg In(1 – XXAR)
(L)
AR°C'
In(1 - Х AR)
(19B.7-3)
Ar lr=R
АВ
dt
where c is the molar density of pure liquid A. Show that when this equation is integrated
from t = 0 to t = to (the time for complete evaporation of the droplet), one gets
to =
2cD
AB In[1/(1 – xAR)]
(19B.7-4)
Does this result look physically reasonable?](https://content.bartleby.com/qna-images/question/7bd3d356-f8d2-4558-9417-c4406f3e0630/d5aa2cf4-43fa-4233-ae59-3a8d4cb8f7b1/lhf45rl_processed.jpeg)
Transcribed Image Text:19B.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
infinite distance from the droplet.
gas phase is x,
AR at r = R and zero at an
(a) Assuming that R is constant, show that at steady state
AB 2 dx
dr
R²NArlr=R
(19B.7-1)
XA
where Nl-R is the molar flux in the r direction at the droplet surface, c is the total molar
concentration in the gas phase, and DAR 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
АВ
RNArlr=R =
= -cD
АВ
In(1 - XAR)
(19B.7-2)
(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
d
-TR°C) = 47R°N olar = -4rRcDg In(1 – XXAR)
(L)
AR°C'
In(1 - Х AR)
(19B.7-3)
Ar lr=R
АВ
dt
where c is the molar density of pure liquid A. Show that when this equation is integrated
from t = 0 to t = to (the time for complete evaporation of the droplet), one gets
to =
2cD
AB In[1/(1 – xAR)]
(19B.7-4)
Does this result look physically reasonable?
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