Problems and Solutions
Chapter 2
PvT Behavior of Pure Components
Textbook Examples:
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02.05
02.06
(the link to the reference
"02.EOS-ethylene.mcd" has to be deleted and added new via Insert -
Reference !)
02.07
Missing due to convergence problems that need to be solved.
02.08
Part a-c
Part d
02.09
Additional Problems:
P02.01
Calculate the compressibility factor and the molar volume of
methanol steam at 200°C and 10 bar
a) using the ideal gas law
b) with the virial equation truncated after the 3rd
virial coefficient
(virial coefficients: B=-219 cm3/mol; C=-17,300 cm6/mol2)
P02.02 Pressure
and Compressibility Factor of Ethylene Using the Virial and the
Peng-Robinson Equation of State
A container with a volume of V=0.1 m3 is filled with m
= 10 kg ethylene at a temperature of T = 300 K. What will be the
pressure and compressibility factor of the gas? Use the virial equation
with only two coefficients and the Peng-Robinson equation of state to
describe the PVT-behavior. (virial coefficient: B=-138 cm3/mol,
all other properties are given in Appendix A)
Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS
P02.03 Calculation
of the 2nd Virial Coefficient from the VdW EOS
Derive an expression for the 2nd virial coefficient
based on the van der Waals equation of state.
Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS
P02.04 Volume
Dependence of the Internal Energy from the VdW EOS
Derive an expression for the volume dependence of the internal
energy U at constant temperature based on the van der Waals equation of
state.
Mathcad (2001) - Solution as XPS
P02.05 Pressure
of CO2 from Ideal Gas Law,
Virial Equation and Redlich-Kwong EOS
Calculate the pressure of 1 mol CO2 in a container of
2.5 dm3 at 40°C via the
a) ideal gas law
b) virial equation
c) Redlich-Kwong-equation
(virial coefficient: B=-110 cm3/mol; for all other
required properties see Appendix A)
Mathcad (2001) - Solution as XPS
P02.06
Derivation of Residual Functions Using the Redlich-Kwong
EOS
Derive the expressions for the residual functions (h-hid),
(s-sid), (g-gid) using the Redlich-Kwong equation
of state.
Mathcad (2001) - Solution as XPS
P02.07 Change
in Enthalpy During Isothermal Compression
Calculate the change in enthalpy of 1 mol of liquid ethanol
during isothermal compression from 1 bar to 100 bar at a temperature of
25°C. The compressibility coefficient (1.14·10-4
bar-1), the thermal expansion coefficient (1.1·10-3
K-1) and the molar volume (58.04 cm3/mol) are
regarded as constant.
Mathcad (2001) - Solution as XPS
P02.08 Virial
Coefficient Data Via the DDB
Search for experimental 2nd virial coefficient data
for nitrogen in the DDB. Compare the values to the estimation results
from the Tsonopoulos method via DDBSP-Predict. Estimate the Boyle
temperature from the experimental findings.
DDB Explorer Version video
(large),
(medium),
(small)
P02.09 VBA
Program to Calculate Vapor Pressure Curve, Comparison to DDB Data
Retrieve the vapor pressure and the liquid density data for
methane from the DDBSP Explorer Version and export the values to Excel.
Implement a liquid vapor pressure curve calculation for the van der
Waals equation of state in Excel-VBA and compare the results along the
vapor-liquid coexistence curve to the experimental data.
Step 1: DDB Explorer Version - Data retrieval
and Export (large), (medium), (small)
Step 2: Excel document containing data and VBA code
planned for June 2012
P02.10 Estimation
of the Azentric Factor from Critical Data and Normal Boiling Temperature
Estimate the acentric factor of methane, propane, pentane and
heptane using the critical data and normal boiling temperatures given in
Appendix A and discuss the results.
Mathcad (2001) - Solution as XPS
P02.11 Vapor
Pressure Calculation and Slope of the Vapor Pressure Curve via SRK
Calculate the vapor pressure of benzene between 280 and 540 K
using the Soave-Redlich-Kwong equation of state with critical data and
acentric factor given in Appendix A. Compare the slope of the vapor
pressure curve in the log(P) vs. 1/T diagram with the slope calculated
via the vapor pressure correlation also given in Appendix A.
Mathcad (2001) - Solution as XPS
P02.12 Cooling
Duty for a Gaseous Propylene Stream Using Peng-Robinson
In a heat exchanger, gaseous propylene is cooled down from
J1
= 90°C, P1 = 20 bar to
J2=60°C.
The pressure drop across the heat exchanger is
DP
= 2 bar. How much cooling water is necessary? The supply and return
temperatures of the cooling water are
JCWS
= 30°C and
JCWR
= 40°C, respectively. Use the Peng-Robinson equation of state for
propylene and the function given for cPL in
Appendix A.
Mathcad (2001) - Solution as XPS
P02.13 Change
of Pressure when Heating Liquid Water in a Constant Volume Using a High
Precision EOS
A closed vessel filled completely with liquid water at
J1
= 25°C, P1 = 1 bar. Due to solar radiation, it is
heated up to
J2=60°C.
What pressure P2 is built up? Use a high-precision equation
of state. Calculate the transferred heat.
Mathcad (2001) - Solution as XPS
P02.14 Ideal
Gas Enthalpy Calculation for Temperature and Pressure Change
An ideal gas is heated up from T1 to T2 in
a heat exchanger. The pressure drop is
DP
= P2-P1 > 0. Why can the duty be calculated with
the isobaric heat capacity by q12 = cPid
×(T2-T1),
although a pressure drop occurs?
P02.15 Relationship
to Calculate the Heat Capacity at Constant Pressure from the Second
Derivative of the Gibbs Energy with Temperature
Show that the relationship
P02.16 Heat
Duty for Isobaric and Isochoric Heating of a Gas Using a High Precision
Equation of State
A vessel is filled with nitrogen at
J1
= 20°C and P1 = 1 bar. With the help of a high
precision equation of state, calculate the duty
a) if the drum is
heated up isobarically to
J2
= 100°C.
b) if the drum is
heated up isochorically to
J2
= 100°C.
Interpret the results.
Mathcad (2001) - Solution as XPS
P02.17 Relationship
to Calculate the Entropy from the Derivative of the Gibbs Energy with
Temperature at Constant Pressure
Show that the relationship
P02.18 Vapor
Pressure of Acetone from 7 Different EOS
Calculate the vapor pressure of acetone at T1 = 260 K,
T2 = 360 K and T3 = 450 K using
a) the vapor
pressure equation listed in Appendix A
b) a high-precision
equation of state
c) the Peng-Robinson
equation of state
d) the
Redlich-Kwong-Soave equation of state
e) the Redlich-Kwong
equation of state
f) the PSRK equation
of state
g) the VTPR equation
of state
What are the conclusions of the results ?
(All required parameters can be found in the appendix.)
Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS
P02.19 Density
of Liquid Methanol from 7 Different EOS
Calculate the saturated density of liquid methanol at T1
= 300 K and T2 = 430 K using
a) the density
equation listed in Appendix A
b) a high-precision
equation of state
c) the Peng-Robinson
equation of state
d) the
Redlich-Kwong-Soave equation of state
e) the Redlich-Kwong
equation of state
f) the PSRK equation
of state
g) the VTPR equation
of state
What are the conclusions of the results ?
(All required parameters can be found in the appendix.)
Mathcad (2001) - Solution (zip) (planned for June 2012
Mathcad (2001) - Solution as XPS
P02.20 Compressibility
Factor of Gaseous Propylene Via Tsonopoulos, Peng-Robinson and a High
Precision Equation of State
Calculate the compressibility factor z of gaseous propylene at P1
= 2 bar and P2 = 10 bar at T = 293.15 K, using the
Tsonopoulos and the Peng-Robinson equations of state. Check the results
with a high-precision equation of state. All required parameters can be
found in the appendix.
Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS
P02.21 Required
Input Parameters for the Calculation of Saturated Vapor Enthalpy
Make a list of all the input parameters necessary for the
calculation of the enthalpy of the saturated vapor of a pure substance
if
a) the Peng-Robinson
equation of state
b) the vapor
pressure equation in combination with the Peng-Robinson equation of
state
c) the VTPR equation
of state
is used. The vapor pressure itself shall not be an input parameter.
P02.22 Saturated
Vapor Fugacity, Vapor and Liquid Volumes and Heat of Vaporization Using
Soave-Redlich-Kwong
Calculate
a) the fugacity fs
at the saturation state
b) the molar volumes
vL and vV in the saturation state
c) the enthalpy of
vaporization
for n-butane, benzene and water at
J1=30°C,
J2=80°C
and
J3=130°C
using the Soave-Redlich-Kwong equation of state. All required parameters
can be found in the Appendix.
Mathcad (2001) - Solution as XPS
P02.23 Standard
Gibbs Energy of Formation for the Liquid Phase from the Value for the
Ideal Gas State at 1 atm
In Appendix A, the Standard Gibbs energy of formation at
J=25°C
and P = 1 atm is reported to be
Mathcad (2001) - Solution as XPS