CMPSC 201 – FA16 Project #1

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Objective: Write a C++ program that solves the Van der Waals equation of state using the
Newton-Raphson method.
Program Description:
A more realistic equation of state than the ideal gas law is the Van der Waals equation:
gas constant, P = pressure, T = temperature, and Vˆ is the volume per unit mole of
material (molar volume).
The values of the Van der Waals constants for air are:
liter 2 a 1.33 atm mole
b 0.0366 liter mole
a
V b R T
where a and b are parameters for a given gas, R = 0.08206 (liter atm/(mole K)) is the
universal
P V2
ˆ

ˆ
CMPSC 201 – FA16
Air is contained in a vessel at T = 170 K and P = 50 atm. Compute the molar volume of the
air Vˆ ˆ
using the Van der Waals equation. You can use the ideal gas law PV RT to obtain an
initial estimate for Vˆ with which to start the iteration.
To implement the Newton-Raphson method for this problem, rewrite the equation as a
function of the volume:
a
P V2
'ˆ
f (Vn)
'ˆˆ where f (V ) is the derivative of the function with respect to V :
ˆ
f'VP a 2ab
ˆ
ˆˆ V b R T 0 f ( V )
The each successive iteration will be obtained by using:
ˆ

f (V )
ˆˆ
VV n1 n
n
ˆ2 ˆ3
VV
Continue iterations until the value of Vˆ changes by less than 1% from one iteration to the
next. Test Data: The above values should give you a Vˆ of 0.2101
Notes:
● You will need to have 2 variables to represent the volume.
● Read the problem very carefully to make sure you fully understand what you
are solving
●
for.
● Your program should prompt for a, b, T and P.
● All data should be 4 decimal points of precision.
●
What are you turning in:
1. A printout of your original source code
2. A printout of your output with your program run with ONE of the following
sets of data:
3. Upload your source to the Angel drop box. Be sure you have followed the
rules for naming your cpp file.
4. If you neglect to either upload your file or turn in your paperwork, I will not
grade your project and you will get a zero for the assignment. I assume you
are all adults and I do not have to chase you down for your work.

Material a b P T
H2 0.246 0.02662 150 200
CO2 3.604 0.04278 75 350
H2O 5.460 0.03046 45 65
Graded on:
● Good programming
● Neat & readable code
● Comments
● Use of selection
● Use of repetition
● Logic
●
Recommended Timeline:
Converting the formula to C++ code Calculations
Meaningful variables
Be sure to echo your input values

Output – both results & format Input – prompting & use
Sept 23 Sept 26 Sept 27 Oct 7
Walked through the program and solved it by hand Pseudocode written
Starting writing the program
Program completed and running tests