The Redlich-Kwong equation of state (RK EOS) is: RT a V-b √TV (V + b) P = where P is the pressure, I the absolute temperature, and R the gas constant. The coefficients a and b are given in terms of Tc and Pc for the fluid, by a = 0.42748R² T 2.5/P and b = 0.08664R Tc/Pc You will find the values of V for which P = 9.46 bar (= 946kPa) at T=350K for n-butane,

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The Redlich-Kwong equation of state (RK EOS) is:
P =
RT
a
V-b √TV (V + b)
where P is the pressure, I the absolute temperature, and R the gas constant. The coefficients
a and b are given in terms of Tc and Pc for the fluid, by
a = 0.42748R² T 2.5/P and b = 0.08664R Tc/Pc
You will find the values of V for which P = 9.46 bar (= 946kPa) at T=350K for n-butane,
which has Tc = 421.5K and Pc = 3796kPa. The smallest Vis the liquid phase, while the
largest is the vapor phase (the intermediate value is unstable).
a) From the RK EOS, what must be the dimensions of b? Verify that the formulas for a and
b are dimensionally consistent with the RK EOS. (Hint: from the ideal gas EOS, PV and
RT have the same dimensions.) With P in Pa and T in Kelvin, what are convenient units
for R, b, and V?
b) Plot P versus V, for V ranging from 0.0001 to 0.1 m^3/mol. Use a log scale for V.
Construct the V table to be equally spaced on a log scale, with 20 points per decade. To
do this, start with a table of log10 V values: -4, -3.95, ...-1. Compute and plot P in MPa.
Transcribed Image Text:The Redlich-Kwong equation of state (RK EOS) is: P = RT a V-b √TV (V + b) where P is the pressure, I the absolute temperature, and R the gas constant. The coefficients a and b are given in terms of Tc and Pc for the fluid, by a = 0.42748R² T 2.5/P and b = 0.08664R Tc/Pc You will find the values of V for which P = 9.46 bar (= 946kPa) at T=350K for n-butane, which has Tc = 421.5K and Pc = 3796kPa. The smallest Vis the liquid phase, while the largest is the vapor phase (the intermediate value is unstable). a) From the RK EOS, what must be the dimensions of b? Verify that the formulas for a and b are dimensionally consistent with the RK EOS. (Hint: from the ideal gas EOS, PV and RT have the same dimensions.) With P in Pa and T in Kelvin, what are convenient units for R, b, and V? b) Plot P versus V, for V ranging from 0.0001 to 0.1 m^3/mol. Use a log scale for V. Construct the V table to be equally spaced on a log scale, with 20 points per decade. To do this, start with a table of log10 V values: -4, -3.95, ...-1. Compute and plot P in MPa.
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