TE 303 - HW #4, P3 - COMPUTER ANALYSIS: P-V Data - 20 pts

Measured data for pressure versus volume during the expansion of gases within the cylinder of an internal combustion engine are given in the table below:

Data Point V (cm^3) P (bar)
1 300 15
2 361 12
3 459 9
4 644 6
5 903 4
6 1608 2

Using data from the table and using EXCEL, complete the following:
(a) Determine the value of d such that the data are fit by an equation of the form PVd = constant. (HINT: take the log of both sides and rearrange into a linear equation.) You are expected to extract the value of d from either doing a curve fit with something like least squares, or from the slope or intercept function in Excel for the appropriate graph.

(b) Evaluate analytically the work done by the gases, in kJ, using the appropriate equation from class along with the result from (a).

(c) Using numerical integration of the data, evaluate the work done by the gases, in kJ (NOTE: Be careful about converting your units!). A common numerical integration method is the Trapezoidal Rule for Unevenly Spaced Data. Using this method, you can approximate the integral in the following way:



where Ai is the area of each rectangular interval, and n is the number of rectangular intervals.

For more information on the Trapezoidal Rule, please see the following website: http://oregonstate.edu/~haggertr/487/integrate.htm

For the "analysis" section of your Engineering Model, be sure to compare the different methods for estimating the work used in parts (b) and (c).