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Problem Set

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Write three programs

**The problems are divided into two sets:**
**you must complete at least one from the
more difficult set.**
**Exam Mark Printer**

Write a program to take in a set of ten exam marks from the keyboard,
sort them into increasing numerical order and print them out. The program
should print the student number (assume the marks are entered in order
of increasing student number, so the first mark belongs to student 1, etc.)
alongside the exam mark. The program should produce the output as a printed
list.

**Stirling's Approximation**

logN! = NlogN-N
is Stirling's approximation, used in statistical thermo-dynamics. Write
a program to check this formula for N=10, N=100, N=1000 and N=5000, bearing
in mind that 5000! is much too large a number to store in the computer.

**Fibonacci Series**

The fibonacci series of numbers proceeds as follows 1, 1, 2, 3, 5, 8,
13..... Calculate the first 25 terms and store them in an array, print
out the contents of the array.

**Polar Coordinates**

One set of polar coordinates of a point is given by (r, *q*), where
r is the length of the ray from the origin to the point and *q* is
the measure of an angle from the positive x axis to this ray.

Write a program that reads polar coordinates for a point (in distance
and degrees -not radians) and calculates and displays its rectangular coordinates
(x,y) obtained by using the formulas above.

**Van der Waals Equation**

The van der Waals equation for gases is an extension of the equation
PV=nRT which attempts to take into account the deviation of real gases
from ideal behaviour. The equation is:

in which n is the number of moles of gas, p its pressure (Pa), T the
temperature (K), V the volume (m ), R the gas constant (8.314 J mol-l K-l)
and a and b are constants which measure the deviation from ideality of
the gas behaviour. Rearrange this equation so that it gives p as a function
of V, then write a program that prints a table with p for 10 volumes between
Vl and V2. The variables a, b, T, Vl,V2 and n should be entered from the
keyboard. For Hydrogen a=0.0247 Pa m^{6}mol^{-2} and b=26.6x10^{-6}
m^{3}mol^{-l}. For CarbonDioxide a=0.366 Pa m^{6}mol^{-2}
and b=42.9x10^{-6} m^{3}mol^{-l}.