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Rate Processes - Part 2
Electricity
In a conductor, a voltage difference forces
electrons to jump from atom to atom
Pushing an electron in, forces another electron
out. That electron is forced into the next
atom, which then has to kick one out, and so
on…
The flow rate of charge is called current
See next slide.
Electricity
Vin
e-
Valence
Electrons
e-
e-
e-
e-
Vout
Nucleus
Electricity Analogy 1:
Peas in a straw
The addition of one pea causes a pea to leave
at the other end.
Although the peas can move through the
straw slowly, the effect of adding another pea
is felt immediately.
Electricity Analogy 2:
Gas Flow through Bed of Sand
Pin
Gas flow
heat
Pout
Work
Blower
Vin
Sand Bed
Electron flow
heat
Generator
Resistor
Vout
Work
Electricity
x
Vin
Electron flow
A
Vout
Work
Generator
voltage
charge
current
Vin  Vout
q
i
V
J electron 
 

At A
x
x
Electrical conductivity
Electrical Conductivity
The proportionality constant for electron flux
is called the electrical conductivity.
If material has a high electrical
conductivity, then the charge flows ‘easily’
for a given V. This material is called a
conductor, and makes good wires.
For a material with the same V, if  is
small, the flow is more difficult. This
material is called an insulator, and makes a
good shield around the wires.
Pair Exercise 1
For the SI system, what are the units
of ?
Pair Exercise 2
With V = 500 V, how much
current (A) flows through a
0.005-m diameter aluminum
wire that is 100 km long ?
Pairs Exercise 3
A charge of 0.75 coulombs passes
through a copper wire every 15
seconds. What is the current?
If that wire is 2.00 km long and has a
diameter of 1.00 mm, what is the
potential difference between the two
ends?
Diffusion
Species A
x
Salt
Water
Cin
A
Cout
Fresh
Water
Concentration
Mass (or moles)
Cin  Cout
MA
C
JA 


At
x
x
Diffusivity
Pairs Exercise 4
In the SI system, what are the units of
diffusivity?
Pairs Exercise 5
A 1.00-km long, 0.25-m diameter pipe
connects a freshwater lake to the
ocean. The pipe has been abandoned
for many years. At what rate (kg/yr)
does salt (NaCl) diffuse from the ocean
to the lake? Seawater has a salt
concentration of 35 kg/m3. Assume the
average temperature has been 291 K.
Resistance
Separation
Distance
Driving Force D
x
Resistance  R 


Flow Rate
r
AK
Cross-sectional
Area
Heat
Fluid Flow
Electricity
Diffusion
Rheat
x

Ak
8  x
R fluid 
A2
x
Relectron 
A
x
RA 
A
Proportionality
Constant
Electrical Resistance
Most commonly, “resistance” implies
electrical resistance
x
V
Relectron 

A
i
Voltage Difference

 Ohms 
Current
Ohm’s Law: V=iR
coulombs/s
Pairs Exercise 6
Two batteries are connected in series
(V=1.5 V each) and connected to a
circuit of resistors. An ammeter
measures the current to be 1.5 mA.
What is the resistance in the circuit?
+
V
-
i
Current
black
box
Resistances in Series
R1
R2
R
n
R   Ri  R1  R2
i 1
Resistances in Parallel
R1
R2
R
n
1
1
1
1
  
R i 1 Ri R1 R2
Pairs Exercise 7
Calculate the equivalent resistance
when a 5- and a 10- resistor are
connected in
a. series
b. parallel
Summary
Thermodynamics tells us where a process is
going, and rate processes tell us how long it
takes to get there.
Regardless of whether we are talking about
heat, fluids, electrons, or chemical species:
flow rate and flux are derived from the
same basic equation,
everything flows ‘downhill’ from a higher
to a lower potential; only terminology
changes.