### Textbook Examples:

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02.05
**
Amount of Ethylene in a Bottle if Given Volume at T, P Using a High
Precision Equation of State. **

02.06
**
Isobaric Heating of Ethylene Using a High Precision Equation of
State. **

(the link to the reference
“02.EOS-ethylene.mcd” has to be deleted and added new via Insert –
Reference !)

02.07
**
Zeno line, Joule-Thomson Inversion Curve and Boyle Curve Using a
High Precision Equation of State. **

Missing due to convergence problems that
need to be solved.

02.08
**
Pressure of Steam in a Vessel from Different Equations of State.
**

Part a-c

Part d

02.09
**
Density of Propylene from the Peng-Robinson Equation of State.
**

### Additional Problems:

P02.01
**Compressibility Factor and Molar Volume
of Methanol Steam **

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 3^{rd}
virial coefficient

(virial coefficients: B=-219 cm^{3}/mol; C=-17,300 cm^{6}/mol^{2})

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 m^{3} 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 cm^{3}/mol, all other properties are given in
Appendix A)

Mathcad (2001) –
Solution (zip)
Mathcad (2001) – Solution as XPS

P02.03 ** Calculation
of the 2**^{nd} Virial
Coefficient from the VdW EOS

Derive an expression for the 2^{nd} 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 (zip)

Mathcad (2001) – Solution as XPS

P02.05 **Pressure
of CO**_{2} from Ideal Gas
Law, Virial Equation and Redlich-Kwong EOS

Calculate the pressure of 1 mol CO_{2} in a container
of 2.5 dm^{3} at 40°C via the

a) ideal gas law

b) virial equation

c) Redlich-Kwong-equation

(virial coefficient: B=-110 cm^{3}/mol; for all other
required properties see Appendix A)

Mathcad (2001) –
Solution (zip)

Mathcad (2001) – Solution as XPS

P02.06
** Derivation of Residual Functions Using the Redlich-Kwong
EOS **

Derive the expressions for the residual functions (h-h^{id}),
(s-s^{id}), (g-g^{id}) using the Redlich-Kwong
equation of state.

Mathcad (2001) –
Solution (zip)

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 cm^{3}/mol) are
regarded as constant.

Mathcad (2001) –
Solution (zip)

Mathcad (2001) – Solution as XPS

P02.08 ** Virial
Coefficient Data Via the DDB**

Search for experimental 2^{nd} 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 E**stimation
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 (zip)

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 (zip)

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
J_{1} = 90°C, P_{1} = 20 bar to
J_{2}=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
J_{CWS} = 30°C and
J_{CWR} = 40°C, respectively. Use the
Peng-Robinson equation of state for propylene and the function given
for c_{P}^{L} in Appendix A.

Mathcad (2001) –
Solution (zip)

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
J_{1 }= 25°C, P_{1} = 1 bar. Due to
solar radiation, it is heated up to
J_{2}=60°C. What pressure P_{2} is
built up? Use a high-precision equation of state. Calculate the
transferred heat.

Mathcad (2001) –
Solution (zip)

Mathcad (2001) – Solution as XPS

P02.14 **Ideal
Gas Enthalpy Calculation for Temperature and Pressure Change**

An ideal gas is heated up from T_{1} to T_{2}
in a heat exchanger. The pressure drop is
DP = P_{2}-P_{1} > 0. Why can the duty
be calculated with the isobaric heat capacity by q_{12} = c_{P}^{id}
×(T_{2}-T_{1)}, although a pressure
drop occurs?

textfile

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
is correct.

solution video
(large), (medium), (small)

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
J_{1 }= 20°C and P_{1} = 1 bar. With
the help of a high precision equation of state, calculate the duty

a) if the drum
is heated up isobarically to
J_{2 }= 100°C.

b) if the drum
is heated up isochorically to
J_{2 }= 100°C.

Interpret the results.

Mathcad (2001) –
Solution (zip)

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
is
correct.

solution video (large),
(medium), (small)

P02.18 ** Vapor
Pressure of Acetone from 7 Different EOS**

Calculate the vapor pressure of acetone at T_{1} =
260 K, T_{2} = 360 K and T_{3} = 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) (planned for
June 2012)

Mathcad (2001) – Solution as XPS

P02.19 **Density
of Liquid Methanol from 7 Different EOS**

Calculate the saturated density of liquid methanol at T_{1}
= 300 K and T_{2} = 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 P_{1} = 2 bar and P_{2} = 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)
will be available soon

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.

solution pdf

P02.22 **Saturated
Vapor Fugacity, Vapor and Liquid Volumes and Heat of Vaporization
Using Soave-Redlich-Kwong**

Calculate

a) the fugacity
f^{s} at the saturation state

b) the molar
volumes v^{L} and v^{V} in the saturation state

c) the enthalpy
of vaporization

for n-butane, benzene and water at
J_{1}=30°C,
J_{2}=80°C and
J_{3}=130°C using the Soave-Redlich-Kwong
equation of state. All required parameters can be found in the
Appendix.

Mathcad (2001) –
Solution (zip)

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
. Estimate the Gibbs energy of formation for the liquid
phase at
J=25°C using the vapor pressure equation given in
Appendix A.

Mathcad (2001) –
Solution (zip)

Mathcad (2001) – Solution as XPS