EXAMPLE 6.2-3 Geankoplis, Transport Processes and Unit Operations
Water in the bottom of a narrow metal tube is held at constant temperature of 293 K. The total pressure of air (assumed dry) is 1.01325 x 10 5 Pa (1.0 atm) and the temperature is 293 K (20 oC). Water evaporates and diffuses through the air in the tube and at a given time t, the level is z m from the top. As diffusion proceeds, the level drops slowly. Derive the equation for the time t f for the level to drop from a starting point of z om at t=0 to z f at t=tf Given: T= 293 K 5
P = 1.01325 x 10 Pa (1.0 atm)
Required: Tf
Fundamentals of Heat and Mass Transfer, 6 th edition, Incropera, et. al.
A laboratory apparatus to measure the diffusion coefficient of vapor-gas mixtures consist of a vertical, small diameter column containing the liquid phase that evaporates into the gas flowing over the mouth of the column. The gas flow rate is sufficient to maintain a negligible vapor concentration at the exit plane. The column is 150 mm high, and the pressure and temperature in the chamber are maintained at 0.25 atm and 320 K, respectively.
For calibration purposes, you’ve been asked to calculate the e xpected evaporation rate (kg/m2·h) for a test with water and air under the foregoing conditions using the known value of D AB for the vapor-air mixture.
Given: P = 0.25 atm T = 320 K
Required: Evap. Rate and Foregoing Conditions Solution: System is unicomponent diffusion
Since J B = 0
( ) ( ) ( ) ( ) ∫ ∫ ( ) ( ) ( ) ( ) ( ) ( )( )
For air-gas mixture, from Table 6.2-1, at 101.32 kPa and 315 K
Using the Lennard-Jones equation for the prediction of diffusivity of binary gas pairs (equation 6.2-44, Geankoplis)
At 320 K and 0.25 atm (25.33125 kPa)
Assume saturated condition at the inlet,
) ( ) ( ( ) vapor pressure at 320 K = 0.1056 atm
In terms of kg/m 2 ·h
PROBLEM NO. 19 octoviancletus, Mass Transfer
A vertical glass tube 3 mm in diameter is filled with liquid toluene to a depth of 20mm from the top openend. After 275 hrs at 39.4 °C and a total 19 pressure of 760 mm Hg the level has dropped to 80 mm from the top. Calculate the value of diffusivity. Given: d= 3mm
Z1= 20 mm T = 275 hrs T = 39.4 oC P = 760 mmhg Z2 =80 mm Required: D AB Solution:
D AB = 9.1572 x 10-6 m2/s
ANSWER
Problem No. 20 Octoviancletus, Mass Transfer
A vertical glass tube 3 mm in diameter is filled with toluene to a depth of 2 cm from the top open end. After 275 hours of operation at 303 K and at a total pressure of 1 atm., the level dropped to 7.75 cm from the top. The density of the liquid is 820 kg/m3 and its vapour pressure is at 57 mm Hg under the given operating conditions. Neglecting the counter diffusion of air to replace the liquid, calculate the diffusivity of toluene in air.
Given: d = 3mm
Z1 = 2 cm t = 275 hr P = 1atm T= 303 K Z2 = 7.75 cm
= 820 kg/m3
P A = 57 mmHg
Required: D AB
Solution:
This is case of Pseudo steady state diffusion as there is significant change in the length of diffusion path. Zto = 0.02 m Zt = 0.0775 m t = 275 hrs. vapour pressure is = 57 mm Hg Molal density of liquid, C Al = 820/92 = 8.913 kmol/m 3
x A1 = 57/760 = 0.075, x B1 = 1-0.075 =0.925 x A2 = 0.0; xB2 = 1.0
(xB)lm = [xB2 - xB1] / ln(xB2/ xB1) = [1-0.925]/ln(1/0.9250 = 0.962
C= P/RT = [1.0132 ×10 5]/[8314 × 303] = 0.04022 kmol/m 3
D AB = C Al (xB)lm (Zt 2 - Zto2) C (x A1 - x A2 ) 2t = 8.913 × 0.962 × (0.0775 2 - 0.022) 0.04022×(0.075-0.0) ×2 ×(275 × 3600) DAB = 0.805 × 10-5 m2 /s
ANSWER
CHE Board Problem MAY 1984
A 4 mm diameter tube, 40 cm long, closed at one end and standing vertically on its closed end, is partially filled with a liquid up to 18 mm from the open top. A gentle stream of air is flowing across the top of the tube. Temperature of the liquid remains constant at 17 °C. Diffusion takes place thru the still air in the tube above the liquid. After 4 hours and 10 mins, the liquid level in the tube goes down by 9.5 mm. The vapor pressure of the liquid is 165 mm Hg and atmospheric pressure is 1 atm. Density of the liquid is 790 kg/m3. Molecular weight of the liquid is 58. Calculate the mass diffusivity of the liquid vapor in air. Given: d= 4mm
L = 40 cm
T = 17 oC 790 kg/m3 M = 58 Required: DAB Solution: System is uni-component diffusion
( ) ( ) ( ) ( ) ( ) ∫ ∫ ( ) ( ) Since J B = 0
( ) [ ] ( ) ( ) + ( ) * Equate
and
