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. Using data from the table complete the following:
(a) Determine a value of n such that the data are fit by an equation of the form pvn = Constant
(b) Evaluate analytically the work done by the gases, in kJ. Using Eq. 2.17 along with the result of part (a)
(c) Using graphical or numerical integration of the data, evaluate the work done by the gases, in kJ.
(d) Compare the different methods for estimating the work used in parts (b) and (c). Why are they estimates?

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V (cm') P (bar) Data Point 15 300 2 12 361 459 4 644 903 2 1608