Measured data for pressure versus volume during the compression of a refrigerant within the cylinder of a refrigeration compressor 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 on the refrigerant, in Btu, using Eq.2.17 along with the result of a part (a).
(c) Using graphical or numerical integration of the data, evaluate the work done on the refrigerant, in Btu.
(d) Compare the different methods for estimating the work used in parts (b) and (c). why are they estimates?

V (in.) p (lbf/in.) Data Point 112 13.0 131 11.0 157 9.0 7.0 4 197 270 5.0 424 3.0