January 24, 2012
Chapter 2
Units
Section 2.1
2-1. The following prefixes are officially approved for various multiples of ten:
10 deca D ,
100 hecto H ,
1000 kilo K
106 mega M ,
109 giga G ,
1012 tera T
How would you express the following quantities in te

HANOI UNIVERSITY OF MINING AND GEOLOGY
ECH 51
Material Balances
First Exam
Monday April 15, 9:00-10:30
(Closed book and closed notes, calculators allowed)
Prof. Brian G. Higgins
April 2012
Given for Exam:
Total Mass Balance
t
V HtL
r V +
A HtL
r Hv - wL

HANOI UNIVERSITY OF MINING AND GEOLOGY
ECH 51
Material Balances
First Exam
Monday April 15, 9:00-10:30
(Closed book and closed notes, calculators allowed)
Prof. Brian G. Higgins
April 2012
Given for Exam:
Total Mass Balance
V
t
v
t
w
n A
0
t
Species Mas

UNIVERSITY OF CALIFORNIA
Department of Chemical Engineering and Materials Science
ECH 51
Material Balances
Practice Final Exam
(Closed book and notes; no questions asked or answered)
(Duration: 110 min )
Given for Exam:
Total Mass Balance
Species Mass Ba

HANOI UNIVERSITY OF MINING AND GEOLOGY
ECH 51
Material Balances
Second Practice Exam
(Closed book and closed notes, calculators allowed)
Prof. Brian G. Higgins
April 2012
Given for Exam:
Total Mass Balance
V
t
v
t
w
n A
0
t
Species balance with Reaction

5—13. A vapor mixture of benzene and toluene is slowly cooled inside a constant volume vessel.
Initially the pres sure inside the vessel is BUD mm Hg and the temperature is TD C. As the vessel is
cooled, the pressure inside the vessel decreases. Assmne th

5—24. Small amounts of an inorganic salt contained in an organic ﬂuid stream can be removed by
contacting the stream with pure water as illustrated in Figure 5.24. The process requires that the
organic and aqueous streams be contacted in a mixer that prov

HANOI UNIVERSITY OF MINING AND GEOLOGY
ECH 51
Material Balances
Second Practice Exam
(Closed book and closed notes, calculators allowed)
Prof. Brian G. Higgins
April 2013
Given for Exam:
Total Mass Balance
V
t
v
t
w
n A
0
t
Species balance with Reaction

Ella. Ifthe ﬂat plate illustrated in Figure 3.21: has a unjfenn mm: per unit area equal to urn: the
tetal mass. ef the plate is. given by
mass = was! = WIDE-1L
Lt'the mass per unit are: is given by w{x,}=].the tetal mass is detﬂmjned by the area integral

University of California Davis
Department of Chemical Engineering and Materials Science
ECH 143 at Hanoi University of Mining and Geology, Vietnam
Mass Transfer, October 2014
Units:
Time and Place:
Instructor:
Four (based on the UC Davis quarter system)
T

BGHiggins/ECH140Hanoi_Dec2012
Transient Heat Conduction in a Sphere
Introduction
This notebook deals with the transient heat conduction of a sphere. Mathematica is used in various parts of the analysis, and in the last section of the notebook we illustrat

Hanoi University of Mining and Geology
Chemical Engineering Program
ECH 140 Mathematical Methods
September 2013
Homework Assignment #4: Solution
Problem 1
Consider the following PDE
T
t
2 T
=
r2
+
1 T
r r
, 0<r<1
IC : T Hr, 0L = T1
BC1
T
r
H1, tL = q
(i)

Problem 1.4.7(c)
At equilibrium (or equivalently at steady state), the governing equation and BCs are
d u
du
du
+ x - b = 0, H0L = 0, HLL = 0
dx
dx
dx 2
2
Integrating twice gives
x
x
u HxL = - + b + C1 x + C2
6
2
3
(1)
2
(2)
Next we apply the BCs to det

Problem 1.4.1(g)
The differential equation and BCs at steady state are given by
2 u
u
= 0, u H0L = T, HLL + u HlL = 0
x2
x
The general solution (after integrating twice) is
u HxL = C1 x + C2
(1)
(2)
Applying the BC at x=0 gives
C2 = T,
(3)
At x=L we hav

Second Order ODEs
Problem_2.1
Determine the general solution for the following ODE:
2 y
y
5
+ + y = 0
x2
x
4
Express your answer in terms of trigonometric functions and exponentials with real arguments.
(1)
Solution
This is a linear second order homoge

First Order ODEs
Problem_1.8
The radioactive decay of a substance is described by the following ODE
Y
= -kY
t
(1)
where k is the decay constant (k > 0). If the amount of material at t=0 is Y0 , determine an expression for the
amount of material Y(t) at a

HANOI UNIVERSITY OF MINING and GEOLOGY
Advanced Program in Chemical Engineering
ECH140: Mathematical Methods for Chemical Engineering
First Exam Solution
September 9, 2013 (9:00-11:00 )
(Closed book and notes no cell phones; no questions asked or answered

First Order ODEs
Problem_1.7
The growth of a biological population P(t) is given by the Verhulst Pearl equation
P
P
= k P J1 - N
t
P
(1)
where P is the limiting size of the population, beyond which the population growth is zero. If P0 is the initial
popu

First Order ODE Problems
Problem_1.5
Find the general solution to the following ODE
y
+ 4 y = t2
t
(1)
Solution
Before we begin it is worthwhile to inspect the form of this equation. It is a linear first order ODE with
constant coefficients and an inhom

First Order ODEs
Problem_1.3
Find the general solution of the following ODE
1
Hx2 yL + y = 0
x2 x
(1)
Solution
First we rearrange the equation as follows
Hx2 yL = -x2 y
x
(2)
p
= -p
x
(3)
Then we introduce the new variable p = x 2 y. Our ODE becomes
I

7-2. In a process for the production of formaldehyde, CH 2 O , by catalytic oxidation of methanol,
CH3OH , an equimolar mixture of methanol vapor and air is sent to a reactor in which the catalyst
is finely divided silver supported on alumina. An undesira

Undergraduate Lectures on
ECH140: Mathema9cal Methods for Chemical Engineers
September 2- 17, 2013
Chapter 1: Lecture 2c:
Cooling of a Sphere!
Brian G. Higgins
Department of Chemical Engineering and
Materials Science
U