Use the generalized compressibility chart to estimate z for (a) nitrogen at 40°C and 40 MPa and (b) helium at -200°C and 350 atm. (Don't forget Newton's corrections.)
Thanks.
To estimate the compressibility factor (z) using the generalized compressibility chart, we will need to follow these steps:
Step 1: Determine the reduced temperature (Tr) and reduced pressure (Pr) for the given conditions.
Step 2: Calculate the Newton's correction factor (ψ).
Step 3: Locate the intersection of Tr and Pr on the chart, and read the corresponding z value.
Let's go through these steps for both cases:
(a) Nitrogen at 40°C and 40 MPa:
Step 1: Calculate the reduced temperature:
Tr = (T / Tc)
where T is the actual temperature (40°C = 313.15 K), and Tc is the critical temperature of nitrogen (126.19 K).
Tr = 313.15 K / 126.19 K = 2.48
Calculate the reduced pressure:
Pr = (P / Pc)
where P is the actual pressure (40 MPa), and Pc is the critical pressure of nitrogen (3.39 MPa).
Pr = 40 MPa / 3.39 MPa = 11.80
Step 2: Calculate the Newton's correction factor:
For nitrogen, the Newton's correction factor (ψ) can be estimated using the following equation:
ψ = 0.06125 / (Tr - 0.672)
Substitute the calculated values:
ψ = 0.06125 / (2.48 - 0.672) = 0.032
Step 3: Locate the intersection of Tr = 2.48 and Pr = 11.80 on the generalized compressibility chart and read the corresponding z value (approximately 0.84).
Therefore, the estimated compressibility factor for nitrogen at 40°C and 40 MPa (with Newton's correction) is approximately 0.84.
(b) Helium at -200°C and 350 atm:
Step 1: Calculate the reduced temperature:
Tr = (T / Tc)
where T is the actual temperature (-200°C = 73.15 K), and Tc is the critical temperature of helium (5.2 K).
Tr = 73.15 K / 5.2 K = 14.08
Calculate the reduced pressure:
Pr = (P / Pc)
where P is the actual pressure (350 atm), and Pc is the critical pressure of helium (2.26 atm).
Pr = 350 atm / 2.26 atm = 154.87
Step 2: Calculate the Newton's correction factor:
For helium, the Newton's correction factor (ψ) can be estimated using the following equation:
ψ = 0.0375 / (Tr - 0.540)
Substitute the calculated values:
ψ = 0.0375 / (14.08 - 0.540) = 0.0027
Step 3: Locate the intersection of Tr = 14.08 and Pr = 154.87 on the generalized compressibility chart and read the corresponding z value (approximately 0.87).
Therefore, the estimated compressibility factor for helium at -200°C and 350 atm (with Newton's correction) is approximately 0.87.
Remember to always double-check the values obtained from the chart to ensure accuracy and perform any necessary conversions.