2.1. Three moles of an ideal gas (with temperature-independent CP = (7/2)R, CV = (5/2)R) is contained in a horizontal piston/cylinder arrangement. The piston has an area of 0.1 m2 and mass of 500 g. The initial pressure in the piston is 101 kPa. Determine the heat that must be extracted to cool the gas from 375°C to 275°C at: (a) constant pressure; (b) constant volume.
2.2. One mole of an ideal gas (CP = 7R/2) in a closed piston/cylinder is compressed from Ti = 100 K, Pi = 0.1 MPa to Pf = 0.7 MPa by the following pathways. For each pathway, calculate ΔU, ΔH, Q, and WEC: (a) isothermal; (b) constant volume; (c) adiabatic.
2.3. One mole of an ideal gas (CP = 5R/2) in a closed piston/cylinder is compressed from Ti = 298 K, Pi = 0.1 MPa to Pf = 0.25 MPa by the following pathways. For each pathway, calculate ΔU, ΔH, Q, and WEC: (a) isothermal; (b) constant volume; (c) adiabatic.
2.4. One mole of an ideal gas (CP = 7R/2) in a closed piston/cylinder is expanded from Ti = 700 K, Pi = 0.75 MPa to Pf = 0.1 MPa by the following pathways. For each pathway, calculate ΔU, ΔH, Q, and WEC: (a) isothermal; (b) constant volume; (c) adiabatic.
2.5. One mole of an ideal gas (CP = 5R/2) in a closed piston/cylinder is expanded from Ti = 500 K, Pi = 0.6 MPa to Pf = 0.1 MPa by the following pathways. For each pathway, calculate ΔU, ΔH, Q, and WEC: (a) isothermal; (b) constant volume; (c) adiabatic.
a. What is the enthalpy change needed to change 3 kg of liquid water at 0°C to steam at 0.1 MPa and 150°C?
b. What is the enthalpy change needed to heat 3 kg of water from 0.4 MPa and 0°C to steam at 0.1 MPa and 150°C?
c. What is the enthalpy change needed to heat 1 kg of water at 0.4 MPa and 4°C to steam at 150°C and 0.4 MPa?
d. What is the enthalpy change needed to change 1 kg of water of a water-steam mixture of 60% quality to one of 80% quality if the mixture is at 150°C?
e. Calculate the ΔH value for an isobaric change of steam from 0.8 MPa and 250°C to saturated liquid.
f. Repeat part (e) for an isothermal change to saturated liquid.
g. Does a state change from saturated vapor at 230°C to the state 100°C and 0.05 MPa represent an enthalpy increase or decrease? A volume increase or decrease?
h. In what state is water at 0.2 MPa and 120.21°C? At 0.5 MPa and 151.83°C? At 0.5 MPa and 153°C?
i. A 0.15 m3 tank containing 1 kg of water at 1 MPa and 179.88°C has how many m3 of liquid water in it? Could it contain 5 kg of water under these conditions?
j. What is the volume change when 2 kg of H2O at 6.8 MPa and 93°C expands to 1.6 bar and 250°C?
k. Ten kg of wet steam at 0.75 MPa has an enthalpy of 22,000 kJ. Find the quality of the wet steam.
2.7. Steam undergoes a state change from 450°C and 3.5 MPa to 150°C and 0.3 MPa. Determine ΔH and ΔU using the following:
a. Steam table data.
b. Ideal gas assumptions. (Be sure to use the ideal gas heat capacity for water.)
2.8. Five grams of the specified pure solvent is placed in a variable volume piston. What are the molar enthalpy and total enthalpy of the pure system when 50% and 75% have been evaporated at: (i) 30°C, (ii) 50°C? Use liquid at 25°C as a reference state.
a. Benzene (ρL = 0.88 g/cm3)
b. Ethanol (ρL = 0.79 g/cm3)
c. Water without using the steam tables (ρL = 1 g/cm3)
d. Water using the steam tables
2.9. Create a table of T, U, H for the specified solvent using a reference state of H = 0 for liquid at 25°C and 1 bar. Calculate the table for: (i) liquid at 25°C and 1 bar; (ii) saturated liquid at 1 bar; saturated vapor at 1 bar; (iii) vapor at 110°C and 1 bar. Use the Antoine equation (Appendix E) to relate the saturation temperature and saturation pressure. Use the ideal gas law to model the vapor phase.
a. Benzene
b. Ethanol
c. Water without using the steam tables
d. Water using the steam tables
2.10. One kg of methane is contained in a piston/cylinder device at 0.8 MPa and 250°C. It undergoes a reversible isothermal expansion to 0.3 MPa. Methane can be considered an ideal gas under these conditions. How much heat is transferred?
2.11. One kg of steam in a piston/cylinder device undergoes the following changes of state. Calculate Q and W for each step.
a. Initially at 350 kPa and 250°C, it is cooled at constant pressure to 150°C.
b. Initially at 350 kPa and 250°C, it is cooled at constant volume to 150°C.
2.12. In one stroke of a reciprocating compressor, helium is isothermally and reversibly compressed in a piston + cylinder from 298 K and 20 bars to 200 bars. Compute the heat removal and work required.
2.13. Air at 30°C and 2MPa flows at steady state in a horizontal pipeline with a velocity of 25 m/s. It passes through a throttle valve where the pressure is reduced to 0.3 MPa. The pipe is the same diameter upstream and downstream of the valve. What is the outlet temperature and velocity of the gas? Assume air is an ideal gas with a temperature-independent CP = 7R/2, and the average molecular weight of air is 28.8.
2.14. Argon at 400 K and 50 bar is adiabatically and reversibly expanded to 1 bar through a turbine in a steady process. Compute the outlet temperature and work derived per mole.
2.15. Steam at 500 bar and 500°C undergoes a throttling expansion to 1 bar. What will be the temperature of the steam after the expansion? What would be the downstream temperature if the steam were replaced by an ideal gas, CP/R = 7/2?
2.16. An adiabatic turbine expands steam from 500°C and 3.5 MPa to 200°C and 0.3 MPa. If the turbine generates 750 kW, what is the flow rate of steam through the turbine?
2.17. A steam turbine operates between 500°C and 3.5 MPa to 200°C and 0.3 MPa. If the turbine generates 750 kW and the heat loss is 100 kW, what is the flow rate of steam through the turbine?
2.18. Valves on steam lines are commonly encountered and you should know how they work. For most valves, the change in velocity of the fluid flow is negligible. Apply this principle to solve the following problems.
a. A pressure gauge on a high-pressure steam line reads 80 bar absolute, but temperature measurement is unavailable inside the pipe. A small quantity of steam is bled out through a valve to atmospheric pressure at 1 bar. A thermocouple placed in the bleed stream reads 400°C. What is the temperature inside the high-pressure duct?
b. Steam traps are common process devices used on the lowest points of steam lines to remove condensate. By using a steam trap, a chemical process can be supplied with so-called dry steam, i.e., steam free of condensate. As condensate forms due to heat losses in the supply piping, the liquid runs downward to the trap. As liquid accumulates in the steam trap, it causes a float mechanism to move. The float mechanism is attached to a valve, and when the float reaches a control level, the valve opens to release accumulated liquid, then closes automatically as the float returns to the control level. Most steam traps are constructed in such a way that the inlet of the steam trap valve is always covered with saturated liquid when opened or closed. Consider such a steam trap on a 7 bar (absolute) line that vents to 1 bar (absolute). What is the quality of the stream that exits the steam trap at 1 bar?
2.19. An overall balance around part of a plant involves three inlets and two outlets which only contain water. All streams are flowing at steady state. The inlets are: 1) liquid at 1MPa, 25°C, 
= 54 kg/min; 2) steam at 1 MPa, 250°C, = 35 kg/min; 3) wet steam at 0.15 MPa, 90% quality, = 30 kg/min. The outlets are: 1) saturated steam at 0.8 MPa, = 65 kg/min; 2) superheated steam at 0.2 MPa and 300°C, = 54 kg/min. Two kW of work are being added to the portion of the plant to run miscellaneous pumps and other process equipment, and no work is being obtained. What is the heat interaction for this portion of the plant in kW? Is heat being added or removed?
2.20. Steam at 550 kPa and 200°C is throttled through a valve at a flow rate of 15 kg/min to a pressure of 200 kPa. What is the temperature of the steam in the outlet state, and what is the change in specific internal energy across the value, (Uout – Uin)?
2.21. A 0.1 m3 cylinder containing an ideal gas (CP/R = 3.5) is initially at a pressure of 10 bar and a temperature of 300 K. The cylinder is emptied by opening a valve and letting pressure drop to 1 bar. What will be the temperature and moles of gas in the cylinder if this is accomplished in the following ways:
a. Isothermally.
b. Adiabatically. (Neglect heat transfer between the cylinder walls and the gas.)
2.22. As part of a supercritical extraction of coal, an initially evacuated cylinder is fed with steam from a line available at 20 MPa and 400°C. What is the temperature in the cylinder immediately after filling?
2.23. A large air supply line at 350 K and 0.5 MPa is connected to the inlet of a well-insulated 0.002 m3 tank. The tank has mass flow controllers on the inlet and outlet. The tank is at 300 K and 0.1 MPa. Both valves are rapidly and simultaneously switched open to a flow of 0.1 mol/min. Model air as an ideal gas with CP = 29.3 J/mol-K, and calculate the pressure and temperature as a function of time. How long does it take until the tank is within 5 K of the steady-state value?
2.24. An adiabatic tank of negligible heat capacity and 1 m3 volume is connected to a pipeline containing steam at 10 bar and 200°C, filled with steam until the pressure equilibrates, and disconnected from the pipeline. How much steam is in the tank at the end of the filling process, and what is its temperature if the following occurs:
a. The tank is initially evacuated.
b. The tank initially contains steam at 1 bar and 150°C.CopycopyHighlighthighlightAdd NotenoteGet Linklink
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