Calculate P versus molar volume behavior of water at
three different temperatures: 300 K, 400 K and 500 K using
vander Waals equation of state. Your results should show both
extrema.
Using the diagrams you generated in part 1, determine
the equilibrium pressure: the pressure at which the areas
above and below the isobar are identical. Compare your
results with the data reported in the steam tables.
Calculate the pressure exerted by Ar for a molar volume 0.45 L
at 200 K using the van der Waals equation of state. The van der
Waals parameters a and b for Ar are 1.355 bar
dm6 mol-2 and 0.0320
dm3mol-1, respectively. Please write your
answer (unit: bar) with 2 decimals, as 12.23. Please do not add
unit to your answer.
Find compression factor Z for this problem
Using Newton-Raphson method, find the complex root of the
function f(z) = z 2 + z + 1 with with an accuracy of 10–6. Let z0 =
1 − i. write program c++ or matlab
***Please code in Python
Write another code Newton (in double precision)
implementing the Newton-Raphson Method
(copy your Bisect code and modify).
Evaluation of F(x) and F'(x) should be done in a
subprogram FCN(x).
The code should ask for input of: x0, TOL, maxIT
(and should print output similar to Bisect code).
Debug on a simple problem, like x2−3 = 0.
Then use it to find root of F(x) in [1,2] with
TOL=1.e-12.
Now consider the problem of finding zeros of
...
Determine the roots of the following simultaneous nonlinear
equations using multiple-equation Newton Raphson method. Carry out
two iterations with initial guesses of
x1(0)
=0.6 and
x2(0)
=1.2. Calculate the approximate relative error
εa in each iteration by using maximum
magnitude norm (║x║∞).
x1 + 1 - x22 = 0
x12 + x22 – 5 =
0
Let . If we use Accelerated Newton-Raphson method to approximate
the root of the equation , which of the following(s) is/are
ture:
(I) is multiple root of order
(II) Accelerated Newton-Raphson formula is :
(III) The sequence obtained by the Accelerated
Newton-Raphson method converge to the
root quadratically.
Consider the Newton-Raphson method for finding root of a
nonlinear function
??+1=??−?(??)?′(??), ?≥0.
a) Prove that if ? is simple zero of ?(?), then the N-R iteration
has quadratic convergence.
b) Prove that if ? is zero of multiplicity ? , then the N-R
iteration has only linear convergence.
Implement in MATLAB the Newton-Raphson method to find the roots
of the following functions.
(a) f(x) = x 3 + 3x 2 – 5x + 2
(b) f(x) = x2 – exp(0.5x)
Define these functions and their derivatives using the @ symbol.
For example, the function of part (a) should be f=@(x)x^3 + 3*x.^2
- 5*x + 2, and its derivative should be f_prime=@(x)3*x.^2 + 6*x -
5.
For each function, use three initial values for x (choose
between -10...