Rate Processes - Part 1
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Objectives
Know the relationships between rate, flux, and driving forceDefine the proportionality constants for heat, fluid flow, electricity, and diffusion problemsKnow how to compute the rate and flux for heat, fluid flow, electricity, diffusion problemsUnderstand the concept of resistance
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RAT 12
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Terminology
Thermodynamics told us where a process was going
For example, if you put a pot of water over a big enough flame, it will boil…eventually
Rate processes tells us how long it takes to get there
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Rate
Rate is the amount a quantity changes per unit time
Flow rate is the amount of quantity N that flows by a point in a given length of time
t
N
t
Nr
in time Change
Quantity in Change Rate
t
Nr Rate Flow
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Example-Water filling a tank
The volume in the tank changes at a rate r1
The water goes past the pipe outlet at flow rate, r2
For this case, because there is no outlet in the tank, the volume changes at the same rate as the water flows in, thus r1 = r2 = r
Vol
ume,
V
Time, t
V
t
rr r
t
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Flux - rate per unit cross-sectional area
area sectional-cross
rate Flux
A
rJ
area) sectional-ss(time)(cro
amount
At
N
Example: bullets through a target
1 m2
1 second passes 2m· second
bullets 5J
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Driving Force - a potential that can result in a flux
r
A
xDin Dout
x
DDK
x
DK
x
D
A
rJ outin
Proportionality Constant
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Fluxes
Quantity, N Driving Force, D
Heat Temperature
Fluids Pressure
Electric Current Voltage
Chemical Species Concentration
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Heat Flux
Heat, Q, energy flows as a result of a temperature differenceHeat flux, Jheat, is the amount of heat (energy) that flows past a cross sectional area, A, in a given time, t
At
QJheat
Heat
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Heat Flux
HeatVibrating copper atom
Copper rod
Tin=100oC Tout=0oCCross sectionalarea, A
x
Tk
x
TTk
At
QJ outin
heat
Thermal conductivity
Heat
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Thermal Conductivity
The proportionality constant for heat flux is called the thermal conductivity.
If material has a high thermal conductivity, then the heat flux (flow rate per unit area) is high, so the heat flows ‘easily’ for a given T. This material is called a conductor.For a material with the same T, if k is small, the heat flux is smaller, thus the flow is more difficult. This material is called an insulator.
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Pair Exercise 1
For the SI system, what are the units of k?Based on your personal experience, classify the following as conductors or insulators:
AluminumCopperStyrofoam
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Pairs Exercise 2
A 1.00-m long silver rod has a square cross section that is 0.200 m on a side. One end is immersed in boiling water and the other end is immersed in an ice bath. How much heat (J/s) flows down the rod?
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Pairs Exercise 3
A house has brick walls 8.00 cm thick. On a winter day, the temperatures on the inner and outer surfaces of the wall were 20oC and -12oC, respectively. Given that the wall has an area of 120 m2, how much heat (J/s) is lost through the wall?
See Table 12.2 for conductivities
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Fluid Flux
• I n the figure above, the volume of fluid, V,flows as a result of a pressure diff erence.
• Fluid flux, J fl uid, is the volume that flows pasta cross sectional area, A, in a given time, t
V A
xPin Pout
d
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Fluid Flux
Fluid flux is given by the Poiseuille equation:
Where is the viscosity (sort of like thickness, or flow resistance)This equation is valid only for laminar (nonturbulent) flow. The flow is laminar provided
x
PA
x
PPA
tA
VJ outin
fluid
88
2300fluidJd
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Pair Exercise 4
For the SI system, what are the units of ?Which is more viscous, water or molasses?Do gases have viscosity?
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Pairs Exercise 5
Calculate the flowrate (m3/s) of glycerin through a 0.01-m diameter, 20-m long pipe with an inlet pressure of 1.5×105 Pa and an outlet pressure of 1.3×105 Pa.
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Pairs Exercise 6
Use Excel to complete hotplate.doc