## Problems for Matlab Fundamentals

### Wind Chill Calculation

As all Minnesota residents know, both the temperature and wind speed combine to give a temperature called the wind chill. The "standard" formula used to calculate wind chill (w), for a given temperature (t, in degrees F) and wind speed (v, in MPH) is

w = .0817*(3.71 * sqrt(v) + 5.81 -.25*v)*(t-91.4)+91.4

This results in wind chill tables as below (linked from USA Today):

For more information, see the USA Today reference page on wind chills and the formula used to calculate this table.

Below are several tasks that you can use to practice your Matlab skills.

1. Calculate the wind chill (WC) for a temp & wind speed (and compare it to table to make sure it is correct)
2. What is result for wind speed < 5 MPH
3. Make plot of WC versus wind speed
• Make a vector of wind speeds (from 5 - 40 MPH in steps of 5)
• Calculate WC for these speeds at a given temperature (will need to use array arithmetic)
• Plot curve of WindSpeed versus WC for this temperature
• Calculate WC for another temperature & overlay on this graph
• Label your graph appropriately
4. Repeat the step above by making a script file which
• Asks for Temperature
• Creates a vector of wind speeds (5-40 MPH)
• Calculates wind chill at this temp
• Plots and labels the graph
5. Repeat the previous plot for speeds of 5 - 200 MPH and note what this means
6. Make surface plot of WC versus wind speed & temperature
• Use meshgrid to calculate table of WC versus wind speed & temp
• Plot the surface
7. Print out WC table after appending on a row of wind speeds and column of temperatures
8. Print out a subrange from 15-30 MPH
9. Use the solve command (discussed in the handout on symbolic math) to determine the wind speed needed to give a particular wind chill at a given temperature (or at given wind speed).

### Non-Ideal Gas (van der Waals equation)

In our Matlab Fundamentals handout, we used the Ideal Gas equation. An equation of state for a non-ideal which is commonly used is the van der Waals equation for 1 mol of gas

P = (R*T)/(V-b) - a/(V^2)

P = Pressure in Atmospheres

R = 0.0821 Atm*Liters/Mol*Kelvin

T = Temperature in Kelvin

V= Volume (in Liters)

The a and b values are

Ideal Gas: a = 0, b = 0 (so it reduces to ideal gas equation)

Nitrogen: a = 16.4349 b = 0.0386

Oxygen: a = 16.5896 b = 0.0318

1. For T=300 K and V=10L, calculate the pressure for nitrogen and oxygen and compare the results with ideal gas
2. Plot the pressure for oxygen & nitrogen for a range of volumes from 0.1L to 10L (in steps of 0.05L) and compare to ideal gas
3. Plot the ratio of the pressure of nitrogen to oxygen and note what happens as the gas is compressed to about 1 L. At this volume, the partial pressure of nitrogen would be much larger than that of oxygen. This is why a scuba diver must be careful when they dive too deep. (With some further study, we could qualitatively reproduce the dive tables).

### Williamsport, Maryland High School Activities

Williamsport High School http://isaac.williamsport.wa.k12.md.us/~ctrout/sciproj/matlab.html has a variety of interesting programs and activities that you can look through. In particular, look over the periodic table activity

Electronic Copy: http://physics.gac.edu/~huber/matlab/mtlabpr1.htm
Revised: 28-JAN-97 by Tom Huber, Physics Department, Gustavus Adolphus College.