Assignment # 4:
Basic Maple Techniques
CENG303
Due by
Reading Assignment:
A Set of Problems demonstrating some more capabilities of Maple:
Laboratory Problems
These problems may be completed with help from any user on Owlnet. You may not
copy anyone else's work, but you can get other users to give you suggestions
and point out mistakes that should be corrected.
1) Use Maple to solve the problem discussed in Example 4.2-1 of Felder and
Rousseau.
2) Use Maple to solve the differential equation derived in Example 11.2-1 in Felder and Rousseau. Note that there may be a couple of typos in this problem in Felder.
3) Use Maple to solve the set of equations given in Example A.2-3 in Felder and Rousseau.
4) Start with the first value for the gas constant in the list on the back
cover of Felder and Rousseau your text.
Use Maple to verify the value given in terms of cubic feet, atmospheres,
lb-moles and degrees Rankine in the same table. Use the following symbols for
the units involved in this problem:
Use the unit conversion factors shown on the inside front cover of the text.
5) Use Maple to integrate the heat capacity data in Example A.3-1 in Felder and Rousseau.
6) Suppose we have a binary solution of two compounds: A and B. The
molecular weights of the compounds are: MA and MB. In one
cubic meter of the solution, there is rA kg of A and rB
kg of B. The total mass density is rtot and is the sum of rA and rB.
The mass fraction of A is wA and is rA/r.
Analogous to the mass quantities: molar quantities may be defined: cA
and cB for molar concentrations of the species and ctot for the
total. Thus cA = rA/MA and c = cA +
cB. Define xA and xB as the mol fractions in
the solution.
The molecular weight of the mixture is defined as Mtot=r/c.
From these basic definitions, use Maple to show
that:
Test Problems
You may work these problems with help ONLY from the course instructor and your
TA.
1)
a) A frequently used equation for ideal gas heat capacity is:
Cp=A + B*((C/T)/sinh(C/T))^2 +D1*((E1/T)/cosh(E1/T))^2
(Note
that D1 and E1 are used rather than D & E since Maple reserves those names
for differentiation and exponentiation.)
Suppose we want to integrate this
relation for Cp between the limits T1 and T2. Determine whether Maple can find
a closed form for this specific integral over arbitrary limits in terms of the
symbols: A, B, C, D1, E1, T1 and T2.
b) For a certain compound, we are given that:
A=7.214e+04, B=1.815e+05, C=2030, D1=1.314e+05, E1=860 for T in K.
The equation is supposed to be valid for the range: T= 298.15 to 1500K and it is reported that
at 298.15K, Cp = 8.5754e+04 J/kmol/K and