1. An air freshener (Figure 1) is used to deliver a pleasant vanilla fragrance in a room. The device consists of a rod that is 1 cm in diameter and 5 cm in length. The rod is composed of a solid mixture containing a volatile aromatic substance that smells like vanilla. A heating element in the center of the rod (0.5 cm in diameter), maintains a constant surface temperature of 313 K to evaporate the aromatic substance. Air at 298 K flows perpendicular to the rod at a velocity of 0.2 m.s¹, and the aroma vapours are immediately diluted to a very low concentration. The density of the gel is 1.1 g.cm³, and the initial loading of the aromatic compound in the solid is 40 mol% (i.e. 40 in 100). The diffusion coefficient of the volatile substance generating the aroma, which approximates the properties of benzaldehyde, is 0.08 cm².s¹ in air at 40 °C. The vapour pressure of this substance is 428 Pa at 40 °C, and its molecular weight is 106 g.mol-1. Assume that the release of the aromatic compound is controlled by the convective transport across the gas film surrounding the rod, and that the diameter of the rod remains constant. Neglect internal diffusion of the aroma substance within the rod itself. Therefore, the correlation used to study the sublimation from a cylinder into air flowing normal to it axis is k&P (Sc) 0.56 kc(Sc) 0.56 GM V∞ = 0.281(Rep)-0.4 which is valid for 400 < ReD < 25,000 and 0.6 < Sc < 2.6. In this correlation, P is the system total pressure and GM is the superficial molar velocity of the gas flowing normal to the cylinder in units of kg.mol.m².s¹. The Reynolds number for flow normal to a solid cylinder, Red, is defined as ReD = pvood μ Where d is the cylinder diameter, v∞ is the fluid velocity normal to the solid cylinder, and p and μ for the gas stream evaluated at the film average temperature. To correct the diffusivity of A for temperature 3 3 Tƒ 2 Tw + Too\2 2 DAB = DAB = DAB TDAB TDAB Where TDAB is the temperature at which the diffusivity is obtained, Tf the average temperature in the film, Tw temperature at the wall and T∞ the free-stream temperature. Air flow (25°C) 0.2 m/s Heated rod (40°C) Wall socket 1 cm 5 cm т Figure 1. Air freshener schematic Air duct Solid fragrance a) What is the initial rate of aroma delivery to the surrounding air in g.h¹? Pair Voo and WA = NAA Hint: GM = MMair b) How long can the air freshener provide fragrance? (d²-d²)pxa ρχα m Hint: m = and t = MM WA [10 marks] [15 marks]
1. An air freshener (Figure 1) is used to deliver a pleasant vanilla fragrance in a room. The device consists of a rod that is 1 cm in diameter and 5 cm in length. The rod is composed of a solid mixture containing a volatile aromatic substance that smells like vanilla. A heating element in the center of the rod (0.5 cm in diameter), maintains a constant surface temperature of 313 K to evaporate the aromatic substance. Air at 298 K flows perpendicular to the rod at a velocity of 0.2 m.s¹, and the aroma vapours are immediately diluted to a very low concentration. The density of the gel is 1.1 g.cm³, and the initial loading of the aromatic compound in the solid is 40 mol% (i.e. 40 in 100). The diffusion coefficient of the volatile substance generating the aroma, which approximates the properties of benzaldehyde, is 0.08 cm².s¹ in air at 40 °C. The vapour pressure of this substance is 428 Pa at 40 °C, and its molecular weight is 106 g.mol-1. Assume that the release of the aromatic compound is controlled by the convective transport across the gas film surrounding the rod, and that the diameter of the rod remains constant. Neglect internal diffusion of the aroma substance within the rod itself. Therefore, the correlation used to study the sublimation from a cylinder into air flowing normal to it axis is k&P (Sc) 0.56 kc(Sc) 0.56 GM V∞ = 0.281(Rep)-0.4 which is valid for 400 < ReD < 25,000 and 0.6 < Sc < 2.6. In this correlation, P is the system total pressure and GM is the superficial molar velocity of the gas flowing normal to the cylinder in units of kg.mol.m².s¹. The Reynolds number for flow normal to a solid cylinder, Red, is defined as ReD = pvood μ Where d is the cylinder diameter, v∞ is the fluid velocity normal to the solid cylinder, and p and μ for the gas stream evaluated at the film average temperature. To correct the diffusivity of A for temperature 3 3 Tƒ 2 Tw + Too\2 2 DAB = DAB = DAB TDAB TDAB Where TDAB is the temperature at which the diffusivity is obtained, Tf the average temperature in the film, Tw temperature at the wall and T∞ the free-stream temperature. Air flow (25°C) 0.2 m/s Heated rod (40°C) Wall socket 1 cm 5 cm т Figure 1. Air freshener schematic Air duct Solid fragrance a) What is the initial rate of aroma delivery to the surrounding air in g.h¹? Pair Voo and WA = NAA Hint: GM = MMair b) How long can the air freshener provide fragrance? (d²-d²)pxa ρχα m Hint: m = and t = MM WA [10 marks] [15 marks]
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:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
Related questions
Question
Transcribed Image Text:1.
An air freshener (Figure 1) is used to deliver a pleasant vanilla fragrance in a room. The device
consists of a rod that is 1 cm in diameter and 5 cm in length. The rod is composed of a solid mixture
containing a volatile aromatic substance that smells like vanilla. A heating element in the center of
the rod (0.5 cm in diameter), maintains a constant surface temperature of 313 K to evaporate the
aromatic substance. Air at 298 K flows perpendicular to the rod at a velocity of 0.2 m.s¹, and the
aroma vapours are immediately diluted to a very low concentration. The density of the gel is 1.1
g.cm³, and the initial loading of the aromatic compound in the solid is 40 mol% (i.e. 40 in 100).
The diffusion coefficient of the volatile substance generating the aroma, which approximates the
properties of benzaldehyde, is 0.08 cm².s¹ in air at 40 °C. The vapour pressure of this substance is
428 Pa at 40 °C, and its molecular weight is 106 g.mol-1.
Assume that the release of the aromatic compound is controlled by the convective transport across
the gas film surrounding the rod, and that the diameter of the rod remains constant. Neglect internal
diffusion of the aroma substance within the rod itself. Therefore, the correlation used to study the
sublimation from a cylinder into air flowing normal to it axis is
k&P (Sc) 0.56 kc(Sc) 0.56
GM
V∞
= 0.281(Rep)-0.4
which is valid for 400 < ReD < 25,000 and 0.6 < Sc < 2.6. In this correlation, P is the system total
pressure and GM is the superficial molar velocity of the gas flowing normal to the cylinder in units of
kg.mol.m².s¹. The Reynolds number for flow normal to a solid cylinder, Red, is defined as
ReD
=
pvood
μ
Where d is the cylinder diameter, v∞ is the fluid velocity normal to the solid cylinder, and p and μ for
the gas stream evaluated at the film average temperature.
To correct the diffusivity of A for temperature
3
3
Tƒ
2
Tw + Too\2
2
DAB
=
DAB
= DAB
TDAB
TDAB
Where TDAB is the temperature at which the diffusivity is obtained, Tf the average temperature in the
film, Tw temperature at the wall and T∞ the free-stream temperature.
![Air flow (25°C)
0.2 m/s
Heated rod (40°C)
Wall
socket
1 cm
5 cm
т
Figure 1. Air freshener schematic
Air duct
Solid fragrance
a) What is the initial rate of aroma delivery to the surrounding air in g.h¹?
Pair Voo and WA = NAA
Hint: GM =
MMair
b) How long can the air freshener provide fragrance?
(d²-d²)pxa
ρχα
m
Hint: m =
and t =
MM
WA
[10 marks]
[15 marks]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66d9f0da-d1eb-49b6-afad-829a4a7e1dfe%2Fcaa6d6e3-8792-429e-a24a-2ff4d88c93ee%2F56zkd1t_processed.png&w=3840&q=75)
Transcribed Image Text:Air flow (25°C)
0.2 m/s
Heated rod (40°C)
Wall
socket
1 cm
5 cm
т
Figure 1. Air freshener schematic
Air duct
Solid fragrance
a) What is the initial rate of aroma delivery to the surrounding air in g.h¹?
Pair Voo and WA = NAA
Hint: GM =
MMair
b) How long can the air freshener provide fragrance?
(d²-d²)pxa
ρχα
m
Hint: m =
and t =
MM
WA
[10 marks]
[15 marks]
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