Question Description
USE EXCEL to Consider a fluid that obeys the van der Waals equation of state
𝑝=𝑅𝑇−𝑎1 with𝑉≥𝑏.𝑉−𝑏 𝑉2
Using the reduced variables
𝑇 = 𝑇 , 𝑝 = 𝑝 , and 𝑉 = 𝑉 ,
𝑟𝑇𝑟𝑝 𝑟𝑉𝑐𝑐𝑐
and equations (3), (4) and (5) from the attached file, express the van der Waals equation in the form 𝑝𝑟 =𝑓(𝑉 , 𝑇 ). Use this form to prepare a high-quality graph of the compressibility factor
𝑟𝑟
𝑝𝑉 3𝑝𝑉𝑍==𝑟𝑟,
𝑅𝑇 8𝑇𝑟
versus reduced pressure, 𝑝𝑟, for six isotherms that correspond to values of the reduced temperature
𝑇 =2.0,1.5,1.3,1.2,1.1,and1.0.𝑟
The scale of the axes should be: 0.1 ≤ 𝑍 ≤ 1.1 (y-axis) and 0 ≤ 𝑝𝑟 ≤ 7 (x-axis).
Note: the equations contain the reduced volume, 𝑉 . In order to prepare the graph, for a given value
of 𝑇 we vary the volume (or, better, the logarithm of the volume), we calculate the pressure, 𝑝 ,𝑟𝑟
from the reduced form of the equation of state, and finally we calculate 𝑍. Then we plot 𝑍 vs 𝑝𝑟and we repeat for other values of 𝑇 . This is conveniently done using excel.
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