Who can solve it in one hour? Principals of chemical engineering
ChBE 254 – Chemical Engineering Calculations Fall 2019 – Exam III
Closed book, closed notes. If enough information is not supplied in the problem statement, use your engineering judgment to make an assumption (state the assumption). 1. (20 points)
a. Estimate the heat of vaporization of hexane at 40oC using the Clapeyron Equation.
Given:
vap
vapsat
VT H
dT dP
∆ ∆
=
(Clapeyron Equation)
∆𝑉𝑉𝑣𝑣𝑣𝑣𝑣𝑣 = 0.789 𝑚𝑚3
𝑘𝑘𝑘𝑘
b. Superheated steam is fed to an insulated turbine at 40 bar and 600oC. It exits the turbine at the same elevation, and kinetic energy changes are negligible. The exit steam is at 1 bar and 150oC. What is maximum amount of work recoverable from this stream? Please give your answer in kJ/kg.
0
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Va po
r pr
es su
re (k
Pa )
Temperature (K)
2. (20 points) Phase Diagrams On the attached PXY phase diagram, label:
1. Saturated liquid line 2. Saturated vapor line 3. Liquid phase 4. Vapor phase 5. 2-Phase region
For an overall composition 60% n-octane:
a. What is the vapor phase composition at the bubble point?
b. What is the liquid composition at the dew point?
c. What are the vapor and liquid compositions for an overall system pressure of 60 kPa?
d. What is the system temperature? The Antoine Equation for n-Hexane is:
ln 𝑃𝑃𝑠𝑠𝑣𝑣𝑠𝑠 (𝑘𝑘𝑃𝑃𝑘𝑘) = 13.8193 − 2696.04
𝑇𝑇(℃) + 224.317
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Pr es
su re
(k Pa
)
x1, y1
PXY Diagram for n-Hexane (1) and n-Octane (2)
3. (20 points) Piston and Cylinder Helium gas at 106 kPa and 437 K is located within a cylinder with a piston. Initially the gas occupies 400 L. While a constant force, F, is applied to the end of the piston so that the pressure inside the cylinder is held constant at 106 kPa, 5520 J of heat is transferred to the helium gas. The specific enthalpy of helium gas is given by the approximate relation:
𝐻𝐻�(𝑘𝑘𝑘𝑘/𝑚𝑚𝑚𝑚𝑚𝑚) = 0.0208 ∙ 𝑇𝑇(𝐾𝐾) a. Draw a picture of your system (initial and final conditions). Include all appropriate
labels. Include initial and final temperatures, pressures, and volumes. Use variables to define any unknowns.
b. How many moles of gas are contained in the cylinder?
c. What is the final temperature (K) of the helium gas?
d. What is the final volume (m3) of the helium gas?
e. What is the work (J) done by the gas?
f. What is the change of internal energy of the system? Give your answer in J.
4. (20 points) Open System Energy Balances Saturated steam is produced by addition of liquid water to superheated steam. Use a basis of 300 kg/min of superheated steam at 20 bar and 350oC. Boiling liquid water at 20 bar is used to bring the steam to saturation. Assume that all kinetic and potential energy changes are negligible. The system is adiabatic, and there are no moving parts. Perform mass and energy balances on this system following the steps outlined in the notes. a. Draw a picture of your system. Label input and exit streams and include mass flow rate,
temperature, and pressure. Use variables to define any unknowns.
b. Determine enthalpies for all streams at appropriate conditions. See attached steam table. All enthalpy values in the steam table are in kJ/kg.
c. Write the open system energy balance and eliminate unnecessary terms (include brief justifications).
d. Determine the mass flow rate of added water and the final mass flow rate of saturated steam.
5. (20 points) Mechanical Energy Balances Water is pumped from a reservoir to a tank suspended 12 m above the reservoir. The water flows through the same size pipe throughout the process. Both the reservoir and the tank are open to the atmosphere. If friction in the pipes consumes 20% of the pump energy, determine the mass flow of water if a 2 hp pump is used. Assume the liquid water has a density of 1 g/cm3. a. Draw a picture of your system. Label parameters of interest in a mechanical energy
balance. Use variables to define unknowns.
b. Write the open system mechanical energy balance and eliminate unnecessary terms. Justify any eliminated terms.
c. What is the mass flow rate of water? Please give your answer in kg/min.
Equation Sheet: Mass and Mole Fractions:
total
i
m m
=ix total
i
n n
=iy ∑∑ == 1xy ii Raoult’s Law: 𝑃𝑃𝑖𝑖 = 𝑦𝑦𝑖𝑖 ∙ 𝑃𝑃 = 𝑥𝑥𝑖𝑖 ∙ 𝑃𝑃𝑖𝑖
𝑠𝑠𝑣𝑣𝑠𝑠 Enthalpy: 𝐻𝐻 = 𝑈𝑈 + 𝑃𝑃𝑉𝑉 Ideal Gas Law:
nRTPV =:Extensive RTPV =:Intensive Gibbs Phase Rule: 𝐷𝐷𝐷𝐷 = 2 + 𝑐𝑐 − 𝛱𝛱 − 𝑟𝑟 Closed System Energy Balance Equation: ∆𝑈𝑈 + ∆𝐸𝐸𝐾𝐾 + ∆𝐸𝐸𝑃𝑃 = 𝑄𝑄 + 𝑊𝑊 Open System Energy Balance Equation: ∆�̇�𝐻 + ∆𝐸𝐸�̇�𝐾 + ∆𝐸𝐸�̇�𝑃 = �̇�𝑄 + 𝑊𝑊𝑆𝑆̇ Mechanical Energy Balance Equation: ∆𝑃𝑃 𝜌𝜌
+ ∆𝑢𝑢2
2 + 𝑘𝑘∆𝑧𝑧 + 𝐷𝐷� =
𝑊𝑊𝑆𝑆̇ �̇�𝑚
Steam Table Units: 𝐻𝐻� = specific enthalpy (kJ/kg), 𝑈𝑈� = specific internal energy (kJ/kg), 𝑉𝑉� = specific volume (m3/kg)
Correction: 1 atm = 406.8 inches H2O(l) at 4oC