Name: SID: Discussion Section: Chemical Engineering Thermodynamics 141 – Spring 2011 Thursday, March 31, 2011 Midterm II – 70 minutes – 100 total points One one-sided 8.5”x 11” equation sheet allowed (20 points) 1. Consider propane in vapor-liquid equilibrium. i) (14 points) Using data at 1 bar from the attached table, calculate the boiling point of propane at 10 bar.
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Name: SID: Discussion Section:
Chemical Engineering Thermodynamics 141 – Spring 2011
Thursday, March 31, 2011
Midterm II – 70 minutes – 100 total points
One one-sided 8.5”x 11” equation sheet allowed
(20 points) 1. Consider propane in vapor-liquid equilibrium.
i) (14 points) Using data at 1 bar from the attached table, calculate the boiling point of propane at 10 bar.
ii) (6 points) Based on the table, what is the boiling point of propane at 10 bar? If the calculated boiling point is different from the experimental value, state three reasons for the error.
(45 points) 2. Consider the Linde process for liquefaction of methane shown below. Methane is compressed to 125 bar and 40°C. Then, it is cooled in a heat exchanger, HEX-1, by a vapor compression cycle using propane as the working fluid. After HEX-1, the methane is further cooled in heat exchanger 2 (HEX-2) using the saturated vapor from the flash drum. The cooled methane is throttled (TV-1) to 1 bar. The mixture of liquid and gaseous methane is sent to a flash drum, where the liquid methane (stream 9) is shipped away and the gas (stream 7) goes through HEX-2 and is recycled to the beginning of the liquefaction process. HEX-1 is the evaporator of a vapor compression cycle and operates at 2 bar. The condenser of this cycle operates at 12 bar. Assume that the effluent of the evaporator (stream 11) is saturated vapor and the effluent of the condenser is saturated liquid. The mass flow rate of methane entering the process (stream 8) is 5 kg/s and ΔTmin = 5.45°C between the cold and hot streams in HEX-1. The temperature of methane at 1 bar exiting HEX-2 (stream 7) is -10°C. See attached tables for thermodynamic data for methane and propane. Consider the enthalpy of liquid methane at 1 bar is zero. Linear interpolation is not necessary and all processes are 100% efficient.
i) (8 points) Qualitatively draw the vapor compression cycle on an lnP-H and T-S diagram. Use the same stream numbers from the schematic and label temperature and pressure
as provided.
ii) (13 points) What is the coefficient of performance (COP) for the vapor compression cycle?
What would the COP be if we had a Carnot refrigerator?
iii) (14 points) What is the mass flow rate of methane at stream 2?
iv) (5 points) What is the circulation rate of propane in the vapor compression cycle?
v) (5 points) What is power rating (in kW) of the compressor in the vapor compression cycle?
(20 points) 3. Consider a container of propane at 1 bar and -42.41°C. i) (10 points) How much would the chemical potential of the liquid and the gas change if the
temperature increased by 0.2°C and the pressure increased by 0.1 bar? What phase(s) would be present in the final state? Entropy and volume changes over this range may be ignored.
ii) (6 points) What is the ratio of initial to final fugacity for the gas phase? Consider
)()( TTT oo .
iii) (7 points) What is the fugacity of liquid propane at a pressure of 300 bar and -5.47oC? The fugacity coefficient of propane is unity at the saturation pressure at this temperature. Assume liquid propane is incompressible.
(17 points) 4. The density (mol/mL) of a propanol-water mixture is:
prx3.01
where xpr stands for the mole fraction of propanol in solution.
i) (10 points) Calculate the partial molar volumes of propanol and water for a propanol – water
mixture with xpr = 0.4.
ii) (7 points) On the V-xpr graph below, show the (a) molar volume of solution, (b) molar volume of pure propanol and water, (c) and the partial molar volume of propanol and water when xpr = 0.4.
Data on saturation curve for propane
Temperature Pressure Density Int Energy Enthalpy Entropy Cp