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engineering
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Fundamentals of Thermodynamics 6th edition Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen - Solutions
Two insulated tanks A and B are connected by a valve. Tank A has a volume of 30 ft3 and initially contains argon at 50 lbf/in 2, 50 F. Tank B has a volume of 60 ft3 and initially contains ethane at 30 lbf/in2, 120 F. The valve is opened and remains open until the resulting gas mixture comes to a
A large SSSF air separation plant takes in ambient air (79% N2, 21% O2 by volume) at 14.7 lbf/in 2, 70 F, at a rate of 2 lb mol/s. It discharges a stream of pure O2 gas at 30 lbf/in 2, 200 F, and a stream of pure N2 gas at 14.7 lbf/in 2, 70 F. The plant operates on an electrical power input of 2000
A tank has two sides initially separated by a diaphragm. Side A contains 2 lbm of water and side B contains 2.4 lbm of air, both at 68 F, 14.7 lbf/in 2. The diaphragm is now broken and the whole tank is heated to 1100 F by a 1300 F reservoir. Find the final total pressure, heat transfer, and total
Consider a volume of 2000 ft3 that contains an air-water vapor mixture at 14.7 lbf/in 2, 60 F, and 40% relative humidity. Find the mass of water and the humidity ratio. What is the dew point of the mixture?
Consider a 10-ft3 rigid tank containing an air-water vapor mixture at 14.7 lbf/in 2, 90 F, with a 70% relative humidity. The system is cooled until the water just begins to condense. Determine the final temperature in the tank and the heat transfer for the process.
Air in a piston/cylinder is at 95 F, 15 lbf/in 2 and a relative humidity of 80%. It is now compressed to a pressure of 75 lbf/in 2 in a constant temperature process. Find the final relative and specific humidity and the volume ratio V2/V1.
A 10-ft3 rigid vessel initially contains moist air at 20 lbf/in 2, 100 F, with a relative humidity of 10%. A supply line connected to this vessel by a valve carries steam at 100 lbf/in 2, 400 F. The valve is opened, and steam flows into the vessel until the relative humidity of the resultant moist
A water-filled reactor of 50 ft3 is at 2000 lbf/in 2, 550 F and located inside an insulated containment room of 5000 ft3 that has air at 1 atm. and 77 F. Due to a failure the reactor ruptures and the water fills the containment room. Find the final pressure.
Atmospheric air at 95 F, relative humidity of 10%, is too warm and also too dry. An air conditioner should deliver air at 70 F and 50% relative humidity in the amount of 3600 ft3 per hour. Sketch a setup to accomplish this, find any amount of liquid (at 68 F) that is needed or discarded and any
Two moist air streams with 85% relative humidity, both flowing at a rate of 0.2 lbm/s of dry air are mixed in a SSSF setup. One inlet flow stream is at 90 F and the other at 61 F. Find the exit relative humidity.
An indoor pool evaporates 3 lbm/h of water, which is removed by a dehumidifier to maintain 70 F, 70% in the room. The dehumidifier is a refrigeration cycle in which air flowing over the evaporator cools such that liquid water drops out, and the air continues flowing
To refresh air in a room, a counter flow heat exchanger is mounted in the wall. It draws in outside air at 33 F, 80% relative humidity and draws room air, 104 F, 50% relative humidity, out. Assume an exchange of 6 lbm/min dry air in a SSSF device, and also that the room air exits the heat exchanger
A 4-ft3 insulated tank contains nitrogen gas at 30 lbf/in 2 and ambient temperatures 77 F. The tank is connected by a valve to a supply line flowing carbon dioxide at 180 lbf/in 2, 190 F. A mixture of 50mole percent nitrogen and 50 mole percent carbon dioxide is to be obtained by opening the valve
Ambient air is at a condition of 14.7 lbf/in 2, 95 F, 50% relative humidity. A steady stream of air at 14.7 lbf/in 2, 73 F, 70% relative humidity, is to be produced by first cooling one stream to an appropriate temperature to condense out the proper amount of water and then mix this stream
A special application requires R-12 at 140C. It is known that the triple-point temperature is 157C. Find the pressure and specific volume of the saturated vapor at the required condition.
In a Carnot heat engine, the heat addition changes the working fluid from saturated liquid to saturated vapor at T, P. The heat rejection process occurs at lower temperature and pressure (T T), (P P). The cycle takes place in a piston cylinder
Ice (solid water) at 3C, 100 kPa is compressed isothermally until it becomes liquid. Find the required pressure.
Calculate the values hFG and sFG for nitrogen at 70 K and at 110 K from the Clapeyron equation, using the necessary pressure and specific volume values from Table B.6.1.
Using thermodynamic data for water from Tables B.1.1 and B.1.5, estimate the freezing temperature of liquid water at a pressure of 30 MPa.
Helium boils at 4.22 K at atmospheric pressure, 101.3 kPa, with hFG 83.3 kJ/kmol. By pumping a vacuum over liquid helium, the pressure can be lowered and it may then boil at a lower temperature. Estimate the necessary pressure to produce a boiling temperature of 1 K and one of 0.5 K.
A certain refrigerant vapor enters an SSSF constant pressure condenser at 150 kPa, 70C, at a rate of 1.5 kg/s, and it exits as saturated liquid. Calculate the rate of heat transfer from the condenser. It may be assumed that the vapor is an ideal gas, and also that at saturation, Vf ! Vg.
A container has a double wall where the wall cavity is filled with carbon dioxide at room temperature and pressure. When the container is filled with a cryogenic liquid at 100 K the carbon dioxide will freeze so the wall cavity has a mixture of solid and vapor carbon dioxide at the sublimation
Small solid particles formed in combustion should be investigated. We would like to know the sublimation pressure as a function of temperature. The only information available is T, hFG for boiling at 101.3 kPa and T, hIF for melting at 101.3 kPa. Develop a procedure that will allow a determination
Derive expressions for (T/v) u and for (h/s) v that do not contain the properties h, u, or s.
Derive expressions for (h/v) T and for (h/T) v that do not contain the properties h, u, or s.
Develop an expression for the variation in temperature with pressure in a constant entropy process, (T/P)s, that only includes the properties P–v–T and the specific heat, Cp.
Determine the volume expansivity, P, and the isothermal compressibility, T, for water at 20C, 5 MPa and at 300C, and 15 MPa using the steam tables. Water at 20oC, 5 MPa (compressed liquid)
Sound waves propagate through a media as pressure waves that cause the media to go through isentropic compression and expansion processes. The speed of sound c is defined by c 2 (P/)s and it can be related to the adiabatic compressibility, which for
Consider the speed of sound as defined in Problem 13.14. Calculate the speed of sound for liquid water at 20C, 2.5 MPa and for water vapor at 200C, 300 kPa using the steam tables.
Find the speed of sound for air at 20C, 100 kPa using the definition in Problem 13.14 and relations for polytropic processes in ideal gases.
A cylinder fitted with a piston contains liquid methanol at 20C, 100 kPa and volume 10 L. The piston is moved, compressing the methanol to 20 MPa at constant temperature. Calculate the work required for this process. The isothermal compressibility of liquid methanol at 20C is 1220
A piston/cylinder contains 5 kg of butane gas at 500 K, 5 MPa. The butane expands in a reversible polytropic process with polytropic exponent, n 1.05, until the final pressure is 3 MPa. Determine the final temperature and the work done during the process.
Show that the two expressions for the Joule–Thomson coefficient J given by Eq. 13.54 are valid.
A 200-L rigid tank contains propane at 9 MPa, 280C. The propane is then allowed to cool to 50C as heat is transferred with the surroundings. Determine the quality at the final state and the mass of liquid in the tank, using the generalized compressibility chart, Fig. D.1
A rigid tank contains 5 kg of ethylene at 3 MPa, 30C. It is cooled until the ethylene reaches the saturated vapor curve. What is the final temperature?
Two uninsulated tanks of equal volume are connected by a valve. One tank contains a gas at a moderate pressure P1, and the other tank is evacuated. The valve is opened and remains open for a long time. Is the final pressure P2 greater than, equal to, or less than P1/2?
Show that van der Waals equation can be written as a cubic equation in the compressibility factor involving the reduced pressure and reduced temperature as
Develop expressions for isothermal changes in enthalpy and in entropy for both van der Waals equation and Redlich-Kwong equation of state.
Determine the reduced Boyle temperature as predicted by an equation of state (the experimentally observed value for most substances is about 2.5), using the van der Waals equation and the Redlich–Kwong equation. Note: It is helpful to use Eqs. 13.47 And 13.48 in addition to Eq. 13.46
Consider a straight line connecting the point P 0, Z 1 to the critical point P PC, Z ZC on a Z versus P compressibility diagram. This straight line will be tangent to one particular isotherm at low pressure. The experimentally
Determine the 2nd virial coefficient B (T) using the van der Waals equation and the Redlich–Kwong equation of state. Find also its value at the critical point (the experimentally observed value is about -0.34 RTC/PC).
One early attempt to improve on the van der Waals equation of state was an expression of the formSolve for the constants a, b, and vc using the same procedure as for the van der Waals equation.
Use the equation of state from the previous problem and determine the Boyle temperature.
Calculate the difference in internal energy of the ideal-gas value and the real-gas value for carbon dioxide at the state 20C, 1 MPa, as determined using the virial equation of state, including second virial coefficient terms. For carbon dioxide we have: B = –0.128 m3/kmol, T (dB/dT) =
Refrigerant-123, dichlorodifluoromethane, which is currently under development as a potential replacement for environmentally hazardous refrigerants, undergoes an isothermal SSSF process in which the R-123 enters a heat exchanger as saturated liquid at 40C and exits at 100 kPa. Calculate
Calculate the heat transfer during the process described in Problem 13.18.
Saturated vapor R-22 at 30C is throttled to 200 kPa in an SSSF process. Calculate the exit temperature assuming no changes in the kinetic energy, using the generalized charts, Fig. D.2 and the R-22 tables, Table B.4
250-L tank contains propane at 30C, 90% quality. The tank is heated to 300C. Calculate the heat transfer during the process.
The new refrigerant fluid R-123 (see Table A.2) is used in a refrigeration system that operates in the ideal refrigeration cycle, except the compressor is neither reversible nor adiabatic. Saturated vapor at -26.5C enters the compressor and superheated vapor exits at 65C. Heat is
A cylinder contains ethylene, C2H4, at 1.536 MPa, 13C. It is now compressed in a reversible isobaric (constant P) process to saturated liquid. Find the specific work and heat transfer.
A piston/cylinder initially contains propane at T = –7C, quality 50%, and volume 10L. A valve connecting the cylinder to a line flowing nitrogen gas at T = 20C, P = 1 MPa is opened and nitrogen flows in. When the valve is closed the cylinder contains a gas mixture of 50% nitrogen,
An ordinary lighter is nearly full of liquid propane with a small amount of vapor, the volume is 5 cm3 and temperature is 23C. The propane is now discharged slowly such that heat transfer keeps the propane and valve flow at 23C. Find the initial pressure and mass of propane and the
An uninsulated piston/cylinder contains propane, C3H6, at ambient temperature, 19C, with a quality of 50% and a volume of 10 L. The propane now expands very slowly until the pressure in the cylinder drops to 460 kPa. Calculate the mass of propane, the work and heat transfer for this process.
A 200-L rigid tank contains propane at 400 K, 3.5 MPa. A valve is opened, and propane flows out until half the initial mass has escaped, at which point the valve is closed. During this process the mass remaining inside the tank expands according to the relation Pv1.4 constant.
A newly developed compound is being considered for use as the working fluid in a small Rankine-cycle power plant driven by a supply of waste heat. Assume the cycle is ideal, with saturated vapor at 200C entering the turbine and saturated liquid at 20C exiting the condenser. The only
A geothermal power plant on the Raft river uses isobutane as the working fluid. The fluid enters the reversible adiabatic turbine, as shown in Fig. P13.42, at 160C, 5.475 MPa and the condenser exit condition is saturated liquid at 33C. Isobutane has the properties Tc
Carbon dioxide collected from a fermentation process at 5C, 100 kPa should be brought to 243 K, 4 MPa in an SSSF process. Find the minimum amount of work required and the heat transfer. What devices are needed to accomplish this change of state?
An insulated cylinder fitted with a frictionless piston contains saturated-vapor carbon dioxide at 0oC, at which point the cylinder volume is 20 L. The external force on the piston is now slowly decreased, allowing the carbon dioxide to expand until the temperature reaches - 30oC. Calculate the
An evacuated 100-L rigid tank is connected to a line flowing R-142b gas, chlorodifluoroethane, at 2 MPa, 100C. The valve is opened, allowing the gas to flow into the tank for a period of time and then it is closed. Eventually, the tank cools to ambient temperature, 20C, at which
A cylinder fitted with a movable piston contains propane, initially at 67oC and 50 % quality, at which point the volume is 2 L. The piston has a cross-sectional area of 0.2 m2. The external force on the piston is now gradually reduced to a final value of 85kN during which process the propane
Consider the following equation of state, expressed in terms of reduced pressure and temperature:What does this equation predict for enthalpy departure from the ideal gas value at the state Pr = 0.4, Tr = 0.9? What does this equation predict for the reduced Boyle temperature?
Saturated liquid ethane at 2.44 MPa enters (SSSF) a heat exchanger and is brought to 611 K at constant pressure, after which it enters a reversible adiabatic turbine where it expands to 100 kPa. Find the heat transfer in the heat exchanger, the turbine exit temperature and turbine work.
A flow of oxygen at 230 K, 5 MPa is throttled to 100 kPa in an SSSF process. Find the exit temperature and the entropy generation.
A cylinder contains ethylene, C2H4, at 1.536 MPa, 13C. It is now compressed isothermally in a reversible process to 5.12 MPa. Find the specific work and heat transfer.
A control mass of 10 kg butane gas initially at 80C, 500 kPa, is compressed in a reversible isothermal process to one-fifth of its initial volume. What is the heat transfer in the process?
An uninsulated compressor delivers ethylene, C2H4, to a pipe, D 10 cm, at 10.24 MPa, 94C and velocity 30 m/s. The ethylene enters the compressor at 6.4 MPa, 20.5C and the work input required is 300kJ/kg. Find the mass flow rate, the total heat transfer and entropy
A distributor of bottled propane, C3H8, needs to bring propane from 350 K, 100 kPa to saturated liquid at 290 K in an SSSF process. If this should be accomplished in a reversible setup given the surroundings at 300 K, find the ratio of the volume flow rates Vin/Vout, the heat transfer and the work
Saturated-liquid ethane at T1 = 14C is throttled into a SSSF mixing chamber at the rate of 0.25 kmol/s. Argon gas at T2 = 25C, P2 = 800 kPa, enters the chamber at the rate of 0.75 kmol/s. Heat is transferred to the chamber from a heat source at a constant temperature of 150oC at a
One kilogram per second water enters a solar collector at 40C and exits at 190C. The hot water is sprayed into a direct-contact heat exchanger (no mixing of the two fluids) used to boil the liquid butane. Pure saturated-vapor butane exits at the top at 80C and is fed to the
A line with a steady supply of octane, C8H18, is at 400C, 3 MPa. What is your best estimate for the availability in an SSSF setup where changes in potential and kinetic energies may be neglected?
A piston/cylinder contains ethane gas, initially at 500 kPa, 100 L, and at ambient temperature, 0C. The piston is now moved, compressing the ethane until it is at 20C, with a quality of 50%. The work required is 25% more than would have been required for a reversible polytropic
The environmentally safe refrigerant R-152a (see Problem 13.65) is to be evaluated as the working fluid for a heat pump system that will heat winter households in two different climates. In the colder climate the cycle evaporator temperature is 20C, and the more moderate climate the
Repeat the calculation for the coefficient of performance of the heat pump in the two climates as described in Problem 13.58 using R-12 as the working fluid. Compare the two results.
One kmol/s of saturated liquid methane, CH4, at 1 MPa and 2k mol/s of ethane, C2H6, at 250C, 1 MPa are fed to a mixing chamber with the resultant mixture exiting at 50C, 1 MPa. Assume that Kay’s rule applies to the mixture and determine the heat transfer in the process.
Consider the following reference state conditions: the entropy of real saturated liquid methane at 100C is to be taken as 100 kJ/k mol K, and the entropy of hypothetical ideal gas ethane at 100C is to be taken as 200 kJ/kmol K. Calculate the entropy per kmol of a
An experiment is conducted at 100C inside a rigid sealed tank containing liquid R-22 with a small amount of vapor at the top. When the experiment is done the container and the R-22 warms up to room temperature of 20C, what is the pressure inside the tank during the
Determine the low-pressure Joule–Thomson inversion temperature from the condition in Eq. 13.54 as predicted by an equation of state, using the van der Waals equation and the Redlich–Kwong equation.
Suppose the following information is available for a given pure substance:Outline the procedure that should be followed to develop a table of thermodynamic properties comparable to Tables 1, 2 and 3 of the steam tables.
The refrigerant R-152a, difluoroethane, is tested by the following procedure. A 10-L evacuated tank is connected to a line flowing saturated-vapor R-152a at 40C. The valve is then opened, and the fluid flows in rapidly, so that the process is essentially adiabatic. The valve is to be closed
An insulated cylinder has a piston loaded with a linear spring (spring constant of 600 kN/m) and held by a pin. The cylinder cross-sectional area is 0.2 m2, the initial volume is 0.1 m3, and it contains carbon dioxide at 2.5 MPa, 0C. The piston mass and outside atmospheres add a force per
A 10- m3 storage tank contains methane at low temperature. The pressure inside is 700 kPa, and the tank contains 25% liquid and 75% vapor, on a volume basis. The tank warms very slowly because heat is transferred from the ambient.a. What is the temperature of the methane when the pressure reaches
Calculate the difference in entropy of the ideal-gas value and the real-gas value for carbon dioxide at the state 20C, 1 MPa, as determined using the virial equation of state. Use numerical values given in Problem 13.30.
Carbon dioxide gas enters a turbine at 5 MPa, 100C, and exits at 1 MPa. If the isentropic efficiency of the turbine is 75%, determine the exit temperature and the second-law efficiency.
A 4- m3 uninsulated storage tank, initially evacuated, is connected to a line flowing ethane gas at 10 MPa, 100C. The valve is opened, and ethane flows into the tank for a period of time, after which the valve is closed. Eventually, the whole system cools to ambient temperature, 0C,
The environmentally safe refrigerant R-142b (see Problem 13.45) is to be evaluated as the working fluid in a portable, closed-cycle power plant. The air-cooled condenser temperature is fixed at 50C, and the maximum cycle temperature is fixed at 180C, because of concerns about
The refrigerant fluid R-21 (see Table A.2) is to be used as the working fluid in a solar energy powered Rankine-cycle type power plant. Saturated liquid R-21 enters the pump, state 1, at 25oC, and saturated vapor enters the turbine, state 3, at 88oC. For R-21: CP0 = 0.582 kJ/kg K and find the
A cylinder/piston contains a gas mixture, 50% CO2 and 50% C2H6 (mole basis) at 700 kPa, 35C, at which point the cylinder volume is 5 L. The mixture is now compressed to 5.5 MPa in a reversible isothermal process. Calculate the heat transfer and work for the process, using the following
A gas mixture of a known composition is frequently required for different purposes, e.g., in the calibration of gas analyzers. It is desired to prepare a gas mixture of 80% ethylene and 20% carbon dioxide (mole basis) at 10 MPa, 25C in an uninsulated, rigid 50-L tank. The tank is initially
A special application requires R-22 at F. It is known that the triple-point temperature is less than 150 F. Find the pressure and specific volume of the saturated vapor at the required condition.
Ice (solid water) at 27 F, 1 atm is compressed isothermally until it becomes liquid. Find the required pressure.
Using thermodynamic data for water from Tables C.8.1 and C.8.3, estimate the freezing temperature of liquid water at a pressure of 5000 lbf/in 2.
Determine the volume expansivity, P, and the isothermal compressibility, T, for water at 50 F, 500 lbf/in 2 and at 500 F, 1500 lbf/in 2 using the steam tables.
Sound waves propagate through a media as pressure waves that cause the media to go through isentropic compression and expansion processes. The speed of sound c is defined by c2 (P/) s and it can be related to the adiabatic compressibility, which for liquid
Consider the speed of sound as defined in Problem 13.79. Calculate the speed of sound for liquid water at 50 F, 250 lbf/in 2 and for water vapor at 400 F, 80 lbf/in 2 using the steam tables.
A cylinder fitted with a piston contains liquid methanol at 70 F, 15 lbf/in 2 and volume 1 ft3. The piston is moved, compressing the methanol to 3000 lbf/in 2 at constant temperature. Calculate the work required for this process. The isothermal compressibility of liquid methanol at 70 F is 8.3
A piston/cylinder contains 10 lbm of butane gas at 900 R, 750 lbf/in 2. The butane expands in a reversible polytropic process with polytropic exponent, n 1.05, until the final pressure is 450 lbf/in 2. Determine the final temperature and the work done during the process.
A 7-ft3 rigid tank contains propane at 1300 lbf/in 2, 540 F. The propane is then allowed to cool to 120 F as heat is transferred with the surroundings. Determine the quality at the final state and the mass of liquid in the tank, using the generalized compressibility charts.
A rigid tank contains 5 lbm of ethylene at 450 lbf/in 2, 90 F. It is cooled until the ethylene reaches the saturated vapor curve. What is the final temperature?
Calculate the difference in internal energy of the ideal-gas value and the real-gas value for carbon dioxide at the state 70 F, 150 lbf/in 2, as determined using the virial equation of state. For carbon dioxide at 70 F,
Calculate the heat transfer during the process described in Problem 13.81. From solution 13.82
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