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Unformatted text preview: EML 5104 Classical Thermodynamics, Spring 2010 Use as cover sheet Name (Print): ___________________________________ UF
ID: ___________________________________ Homework Week 8 and 9 Due March 15 at the begin of class P1: Develop expressions for the volumetric expansivity, β, and the isothermal compressibility, κ, for a) an ideal gas. b) a gas whose equation of state is p(vb)=RT. c) a gas obeying the van der Waals equation. P2: If the specific heat of a gas obeying the van der Waals equation is given at a particular pressure p’ by cv = A+BT, where A and B are constants, develop an expression for the change in specific entropy between any two states 1 and 2: [s(T2, p2)
s(T1, p1)]. P3: Using the Redlich
Kwong equation of state, determine the change in specific enthalpy, in kJ/mol, and entropy, in kJ/mol/K for ethylene (C2H4) between 400 K, 1 bar, and 400 K, 100 bar. Tc=283 K, pc=51.2 bar, Zc=0.270. P4: Nitrogen (N2) enters a compressor operating at steady state at 1.5 MPa, 300 K and exits at 8 MPa, 500 K. If the work input is 240 kJ per kg of nitrogen flowing, determine the heat transfer, in kJ per kg of nitrogen flowing. Ignore kinetic and potential effects. Use departure charts to determine properties. P5: A mixture having a molar analysis of 50% CO2, 33.3% CO, and 16.7% O2 enters a compressor operating at steady state, 37 °C, 1 bar, 40 m/s with a mass flow rate of 1 kg/s and exits at 237 °C, 30 m/s. The rate of heat transfer from the compressor to its surroundings is 5% of the power input. a) Neglecting potential energy effects determine the power input of the compressor, in kW. b) If the compression is polytropic, evaluate the polytropic exponent n and the exit pressure, in bar. Assume ideal gas behavior. P6: One kg of argon at 27 °C, 1 bar is contained in a rigid tank connected by a valve to another rigid tank containing 0.8 kg of O2 at 127 °C, 5 bar. The valve is opened, and the gases are allowed to mix, achieving an equilibrium state at 87 °C. Determine a) the volume of each tank, in m3. b) the final pressure, in bar. c) the heat transfer to or from the gases during the process, in kJ. d) the entropy change of each gas, in kJ/kg Assume ideal gas behavior. P7: A device is being designed to separate into components a natural gas consisting of CH4 and C2H6 in which the mole fraction of C2H6 denoted by y, may vary from 0.05 to 0.5. The device will receive natural gas at 20 °C, 1 atm with a volumetric flow rate of 100 m3/s. Separate streams of CH4 and C2H6 will exit each at 20 °C, 1 atm. Heat transfer between the EML 5104 Classical Thermodynamics, Spring 2010 device and its surroundings occurs at 20 °C. Ignoring kinetic and potential effects, plot verus y the minimum theoretical work input required at steady state, in kW. Assume ideal gas behavior. P8: At steady state, moist air is to be supplied to a classroom at a specified volumetric flow rate and temperature T. Air is removed from the classroom in a separate stream at a temperature of 27 °C and 50% relative humidity. Moisture is added to the air into the room from the occupants at a rate of 4.5 kg/h. The moisture can be regarded as saturated vapor at 33 °C. Heat transfer into the occupied space from all sources is estimated to occur at a rate of 34000 kJ/h. The pressure remains uniform at 1 atm. a) For a supply air volumetric flow rate of 40 m3/min, determine the supply air temperature T, in °C, and the relative humidity. b) Plot the supply air temperature, in °C, and the relative humidity, each versus the supply air volumetric flow rate ranging from 35 to 90 m3/min. Do not use psychrometric chart to determine properties. P9: In the condenser of a power plant, energy is discharged by heat transfer at a rate of 836 MW to cooling water that exits the condenser at 40 °C into a cooling tower. Cooled water at 20 °C is returned to the condenser. Atmospheric air enters the tower at 25 °C, 1 atm, 35% relative humidity. Moist air exits at 35 °C, 1 atm, 90% relative humidity. Makeup water is supplied at 20 °C. For operation at steady state, determine the mass flow rate, in kg/s, of a) the entering atmospheric air. b) the makeup water. Ignore kinetic and potential effects. Use psychrometric chart to determine properties. ...
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