Use the data in Problem 13.4 to solve the following problems:

(a) Create a new column of pressure values at T = 400 K, using linear interpolation.

(b) Create an expanded volume–pressure table with volume measurements every 0.2 m³Â ,with columns corresponding to T = 300 K, T = 400 K, and T = 500 K.

Problem 13.4:

The experiment described in Problem 13.1 was repeated at a higher temperature and the data recorded in the following table:

                                     

Use these data to answer the following questions:

(a) Approximate the pressure when the volume is 5.2 m3 for both temperatures (300 K and 500 K). ( Hint: Make a pressure array that contains both sets of data; your volume array will need to be 6 × 1,and your pressure array will need to be 6 × 2. ) Use linear interpolation for your calculations.

(b) Repeat your calculations, using cubic spline interpolation.

Problem 13.1:

Consider a gas in a piston–cylinder device in which the temperature is held constant. As the volume of the device was changed, the pressure was measured. The volume and pressure values are reported in the following table:

                                      

(a) Use linear interpolation to estimate the pressure when the volume is 3.8 m³Â .

(b) Use cubic spline interpolation to estimate the pressure when the volume is 3.8 m³Â .

(c) Use linear interpolation to estimate the volume if the pressure is measured to be 1000 kPa.

(d) Use cubic spline interpolation to estimate the volume if the pressure is measured to be 1000 kPa.