Problem 10.31

(a) The data in the following table are pressures, in atmospheres, of oxygen gas kept at 25 degrees C and made to occupy various volumes, measured in liters. Draw the scatter plot of (vi, pi). Is the simple linear regression model appropriate?

(b) Chemists believe that the relation between the pressure and volume of a gas at constant temperature is given by p = avb. Draw the scatter plot for the transformed data (xi, yi), where y = ln p and x = ln v. Is the linear regression model appropriate for the transformed data?

(c) Fit a straight line to the transformed data by the method of least squares and determine the point estimates for the parameters a and

b.

(d) Are these results consistent with Boyle’s law for an ideal gas, which states that pv = k? That is, the product of pressure by volume is constant at constant temperature.

Volume (v) Pressure (P) 3.25 7.34 5.00 4.77 5.71 4.18 8.27 2.88 11.50 2.07 14.95 1.59 17.49 1.36 20.35 1.17 22.40 1.06