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engineering
mechanical engineering
Fundamentals of Thermodynamics 6th edition Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen - Solutions
Ethene, C2H4, burns with 150% theoretical air in an SSSF constant-pressure process with reactants entering at P0, T0. Find the adiabatic flame temperature. Discuss.
Solid carbon is burned with stoichiometric air in an SSSF process. The reactants at T0, P0 are heated in a pre-heater to T2 = 900 R with the energy given by the products before flowing to a second heat exchanger, which they leave at T0. Find the temperature of the products T4 and the heat transfer
A closed, insulated container is charged with a stoichiometric ratio of oxygen and hydrogen at 77 F and 20 lbf/in 2. After combustion, liquid water at 77 F is sprayed in such that the final temperature is 2100 R. What is the final pressure?
Blast furnace gas in a steel mill is available at 500 F to be burned for the generation of steam. The composition of this gas is, on a volumetric basis, Component CH4 H2 CO CO2 N2 H2OPercent by volume 0.1 2.4 23.3 14.4 56.4 3.4Find the lower heating value (Btu/ft3) of this gas at 500 F
Two pound moles of ammonia are burned in an SSSF process with x lb mol of oxygen. The products, consisting of H2O, N2, and the excess O2, exit at 400 F, 1000 lbf/in 2. a. Calculate x if half the water in the products is condensed.b. Calculate the absolute entropy of the products at the exit
Graphite, C, at P0, T0 is burned with air coming in at P0, 900 R in a ratio so the products exit at P0, 2200 R. Find the equivalence ratio, the percent theoretical air and the total irreversibility
A small air-cooled gasoline engine is tested, and the output is found to be 2.0 hp. The temperature of the products is measured and found to be 730 F. The products are analyzed on a dry volumetric basis, with the following result 11.4% CO2, 2.9% CO, 1.6% O2 and 84.1% N2. The fuel may be considered
A gasoline engine uses liquid octane and air, both supplied at P0, T0, in a stoichiometric ratio. The products (complete combustion) flow out of the exhaust valve at 2000 R. Assume that the heat loss carried away by the cooling water, at 200 F, is equal to the work output. Find the efficiency of
In Example 14.16, a basic hydrogen–oxygen fuel cell reaction was analyzed at 25C, 100 kPa. Repeat this calculation, assuming that the fuel cell operates on air at 77 F, 14.7 lbf/in 2, instead of on pure oxygen at this state.
Carbon dioxide at 15 MPa is injected into the top of a 5-km deep well in connection with an enhanced oil-recovery process. The fluid column standing in the well is at a uniform temperature of 40C. What is the pressure at the bottom of the well assuming ideal gas behavior?
Consider a 2-km-deep gas well containing a gas mixture of methane and ethane at a uniform temperature of 30C. The pressure at the top of the well is 14 MPa, and the composition on a mole basis is 90% methane, 10% ethane. Determine the pressure and composition at the bottom of the well,
Using the same assumptions as those in developing Eq. d in Example 15.1: Develop an expression for pressure at the bottom of a deep column of liquid in terms of the isothermal compressibility, T, for liquid water at 20C, T=0.0005 [1/MPa]. Use the result of the first question
Calculate the equilibrium constant for the reaction O2 2O at temperatures of 298 K and 6000 K.Reaction O2 2O
Calculate the equilibrium constant for the reaction H2 2H at a temperature of 2000 K, using properties from Table A.8. Compare the result with the value listed in Table A.10.
Plot to scale the values of ink versus 1/T for the reaction 2CO2 2CO O2, write an equation for ink as a function of temperature. 2 CO2 2 CO + 1 O2
Calculate the equilibrium constant for the reaction:2CO2 2CO + O2 at 3000 K using values from Table A.8 and compare the result to Table A.10.
Pure oxygen is heated from 25C to 3200 K in an SSSF process at a constant pressure of 200 kPa. Find the exit composition and the heat transfer.
Pure oxygen is heated from 25C, 100 kPa to 3200 K in a constant volume container. Find the final pressure, composition, and the heat transfer.
Nitrogen gas, N2, is heated to 4000 K, 10 kPa. What fraction of the N2 is dissociated to N at this state?
Hydrogen gas is heated from room temperature to 4000 K, 500 kPa, at which state the diatomic species has partially dissociated to the monatomic form. Determine the equilibrium composition at this state.
Consider the chemical equilibrium involving H2O, H2, CO, and CO2, and no other substances. Show that the equilibrium constant at any temperature can be found using values from Table A.10 only.
One kilo mole Ar and one kilo mole O2 is heated up at a constant pressure of 100 kPa to 3200 K, where it comes to equilibrium. Find the final mole fractions for Ar, O2, and O.
A piston/cylinder contains 0.1 kmol hydrogen and 0.1 kmol Ar gas at 25C, 200 kPa. It is heated up in a constant pressure process so the mole fraction of atomic hydrogen is 10%. Find the final temperature and the heat transfer needed.
Air (assumed to be 79% nitrogen and 21% oxygen) is heated in an SSSF process at a constant pressure of 100 kPa, and some NO is formed. At what temperature will the mole fraction of N .O be 0.001?
Saturated liquid butane enters an insulated constant pressure combustion chamber at 25C, and x times theoretical oxygen gas enters at the same pressure and temperature. The combustion products exit at 3400 K. Assuming that the products are a chemical equilibrium gas mixture that includes
The combustion products from burning pentane, C5H12, with pure oxygen in a stoichiometric ratio exist at 2400 K, 100 kPa. Consider the dissociation of only CO2 and find the equilibrium mole fraction of CO.
Find the equilibrium constant for the reaction 2NO + O2 2NO2 from the elementary reactions in Table A.10 to answer which of the nitrogen oxides, NO or NO2; is the more stable at ambient conditions? What about at 2000 K?
Methane in equilibrium with carbon and hydrogen as: CH4 C + 2H2. Has ink = – 0.3362 at 800 K. For a mixture at 100 kPa, 800 K fined the equilibrium mole fractions of all components (CH4, C, and H2 neglect hydrogen dissociation).Redo the mole fractions for a mixture state of 200
A mixture of 1 kmol carbon dioxide, 2 kmol carbon monoxide, and 2 kmol oxygen, at 25C, 150 kPa, is heated in a constant pressure SSSF process to 3000 K. Assuming that only these same substances are present in the exiting chemical equilibrium mixture, determine the composition of that
Repeat the previous problem for an initial mixture that also includes 2k mol of nitrogen, which does not dissociate during the process.
Complete combustion of hydrogen and pure oxygen in a stoichiometric ratio at P0, T0 to form water would result in a computed adiabatic flame temperature of 4990 K for an SSSF setup. a. How should the adiabatic flame temperature be found if the equilibrium reaction 2H2 + O2 H2O is
Gasification of char (primarily carbon) with steam following coal pyrolysis yields a gas mixture of 1 kmol CO and 1 kmol H2. We wish to upgrade the hydrogen content of this syngas fuel mixture, so it is fed to an appropriate catalytic reactor along with 1 kmol of H2O. Exiting the reactor is a
A gas mixture of 1 kmol carbon monoxide, 1 k mol nitrogen, and 1 k mol oxygen at 25C, 150 kPa, is heated in a constant pressure SSSF process. The exit mixture can be assumed to be in chemical equilibrium w ith CO2, CO, O2, and N2 present. The mole fraction of CO2 at this point is 0.176.
A rigid container initially contains 2 kmol of carbon monoxide and 2 kmol of oxygen at 25C, 100 kPa. The content is then heated to 3000 K at which point an equilibrium mixture of CO2, CO, and O2 exists. Disregard other possible species and determine the final pressure, the equilibrium
One approach to using hydrocarbon fuels in a fuel cell is to “reform” the hydrocarbon to obtain hydrogen, which is then fed to the fuel cell. As a part of the analysis of such a procedure, consider the reforming section a. Determine the equilibrium constant for this reaction at a temperature
In a test of a gas-turbine combustor, saturated-liquid methane at 115 K is to be burned with excess air to hold the adiabatic flame temperature to 1600 K. It is assumed that the products consist of a mixture of CO2, H2O, N2, O2, and NO in chemical equilibrium. Determine the percent excess air used
The van't Hoff equationrelates the chemical equilibrium constant K to the enthalpy of reaction Ho. From the value of K in Table A.10 for the dissociation of hydrogen at 2000 K and the value of Ho calculated from Table A.8 at 2000 K use van€™t Hoff equation to predict the
Catalytic gas generators are frequently used to decompose a liquid, providing a desired gas mixture (spacecraft control systems, fuel cell gas supply, and so forth). Consider feeding pure liquid hydrazine, N2H4, to a gas generator, from which exits a gas mixture of N2, H2, and NH3 in chemical
Acetylene gas at 25C is burned with 140% theoretical air, which enters the burner at 25C, 100 kPa, 80% relative humidity. The combustion products form a mixture of CO2, H2O, N2, O2, and NO in chemical equilibrium at 2200 K, 100 kPa. This mixture is then cooled to 1000 K very
The equilibrium reaction as: CH4 C + 2H2, has ln K = -0.3362 at 800 K and ink = -4.607 at 600 K. By noting the relation of K to temperature shows how you would interpolate ln K in (1/T) to find K at 700 K and compare that to a linear interpolation.
Use the information in Problem 15.31 to estimate the enthalpy of reaction, Ho, at 700 K using Van’t Hoff equation with finite differences for the derivatives.
A step in the production of a synthetic liquid fuel from organic waste matter is the following conversion process: 1 kmol of ethylene gas (converted from the waste) at 25C, 5 MPa, and 2 kmol of steam at 300C, 5 MPa, enter a catalytic reactor. An ideal gas mixture of ethanol,
Methane at 25C, 100 kPa, is burned with 200% theoretical oxygen at 400 K, 100 kPa, in an adiabatic SSSF process, and the products of combustion exit at 100 kPa. Assume that the only significant dissociation reaction in the products is that of carbon dioxide going to carbon monoxide and
Calculate the irreversibility for the adiabatic combustion process described in the previous problem.
In rich (too much fuel) combustion the excess fuel may be broken down to give H2 and CO may form. In the products at 1200 K, 200 kPa the reaction called the water gas reaction may take place: CO2 + H2 H2O + CO
An important step in the manufacture of chemical fertilizer is the production of ammonia, according to the reaction: N2 + 3H2 2NH3 a. Calculate the equilibrium constant for this reaction at 150C. b. For an initial composition of 25% nitrogen, 75% hydrogen, on a mole basis,
A space heating unit in Alaska uses propane combustion is the heat supply. Liquid propane comes from an outside tank at -44C and the air supply is also taken in from the outside at-44C. The airflow regulator is misadjusted, such that only 90% of the theoretical air enters the
One kilo mole of carbon dioxide, CO2, and 1 kmol of hydrogen, H2 at room temperature, 200 kPa is heated to 1200 K at 200 kPa. Use the water gas reaction, see problem 15.36, to determine the mole fraction of CO. Neglect dissociations of H2 and O2.
Consider the production of a synthetic fuel (methanol) from coal. A gas mixture of 50% CO and 50% H2 leaves a coal gasifier at 500 K, 1 MPa, and enters a catalytic converter. A gas mixture of methanol, CO and H2 in chemical equilibrium with the reaction: CO + 2H2 CH3OH leaves the converter at the
Consider the following coal gasifier proposed for supplying a syngas fuel to a gas turbine power plant. Fifty kilograms per second of dry coal (represented as 48 kg C plus 2 kg H) enter the gasifier, along with 4.76 kmol/s of air and 2 kmol/s of steam. The output stream from this unit is a gas
Ethane is burned with 150% theoretical air in a gas turbine combustor. The products exiting consist of a mixture of CO2, H2O, O2, N2, and NO in chemical equilibrium at 1800 K, 1 MPa. Determine the mole fraction of NO in the products. Is it reasonable to ignore CO in the products?
a. Determine the equilibrium composition of the products and also x, the amount of H2 entering the combustion chamber.b. Should another substance(s) have been included in part (a) as being present in the products? Justify your answer.
Butane is burned with 200% theoretical air, and the products of combustion, an equilibrium mixture containing only CO2, H2O, O2, N2, NO, and NO2, exit from the combustion chamber at 1400 K, 2 MPa. Determine the equilibrium composition at this state.
A mixture of 1 kmol water and 1 kmol oxygen at 400 K is heated to 3000 K, 200 kPa, in an SSSF process. Determine the equilibrium composition at the outlet of the heat exchanger, assuming that the mixture consists of H2O, H2, O2, and OH.
One kilo mole of air (assumed to be 78% nitrogen, 21% oxygen, and 1% argon) at room temperature is heated to 4000 K, 200 kPa. Find the equilibrium composition at this state, assuming that only N2, O2, NO, O, and Ar are present.
Acetylene gas and x times theoretical air (x 1) at room temperature and 500 kPa are burned at constant pressure in an adiabatic SSSF process. The flame temperature is 2600 K, and the combustion products are assumed to consist of N2, O2, CO2, H2O, CO, and NO. Determine the value of x.
One kilo mole of water vapor at 100 kPa, 400 K, is heated to 3000 K in a constant pressure SSSF process. Determine the final composition, assuming that H2O, H2, H, O2, and OH are present at equilibrium.
Operation of an MHD converter requires an electrically conducting gas. It is proposed to use helium gas “seeded” with 1.0 mole percent cesium. The cesium is partly ionized (Cs Cs` e) by heating the mixture to 1800 K, 1 MPa, in a nuclear reactor to provide
Plot to scale the equilibrium composition of nitrogen at 10 kPa over the temperature range 5000 K to 15000 K, assuming that N2, N, N`, and e are present. For the ionization reaction N N` e, the ionization equilibrium constant K has been calculated from
One kilo mole of argon gas at room temperature is heated to 20000 K, 100 kPa. Assume that the plasma in this condition consists of an equilibrium mixture of Ar, Ar`, Ar``, and e according to the simultaneous reactions 1) Ar Ar+ + e– 2) Ar+ Ar++ + e– The
Hydrides are rare earth metals, M, that have the ability to react with hydrogen to form a different substance MH x with a release of energy. The hydrogen can then be released, the reaction reversed, by heat addition to the MH x. In this reaction only the hydrogen is a gas so the formula developed
Repeat Problem 15.1 using the generalized charts, instead of ideal gas behavior.
Derive the van’t Hoff equation given in problem 15.28, using Eqs.15.12 and 15.15. Note: the d (g-/T) at constant P for each component can be expressed using the relations in Eqs. 13.18 and 13.19.
A coal gasifier produces a mixture of 1 CO and 2H2 that is then fed to a catalytic converter to produce methane. A chemical-equilibrium gas mixture containing CH4, CO, H2, and H2O exits the reactor at 600 K, 600 kPa. Determine the mole fraction of methane in the mixture.
Dry air is heated from 25C to 4000 K in a 100-kPa constant-pressure process. List the possible reactions that may take place and determine the equilibrium composition. Find the required heat transfer.
Methane is burned with theoretical oxygen in an SSSF process, and the products exit the combustion chamber at 3200 K, 700 kPa. Calculate the equilibrium composition at this state, assuming that only CO 2, CO, H2O, H2, O2, and OH are present. Combustion: CH4 + 2 O2 CO2 + 2 H2O
Carbon dioxide at 2200 lbf/in2 is injected into the top of a 3-mi deep well in connection with an enhanced oil recovery process. The fluid column standing in the well is at a uniform temperature of 100 F. What is the pressure at the bottom of the well assuming ideal gas behavior?
Calculate the equilibrium constant for the reaction O2 2O at temperatures of 537 R and 10 000 R.
Pure oxygen is heated from 77 F to 5300 F in an SSSF process at a constant pressure of 30 lbf/in 2. Find the exit composition and the heat transfer.
Pure oxygen is heated from 77 F, 14.7 lbf/in.2 to 5300 F in a constant volume container, find the final pressure, composition, and the heat transfer As oxygen is heated it dissociates O2 2O ln Keq = -3.069
Air (assumed to be 79% nitrogen and 21% oxygen) is heated in an SSSF process at a constant pressure of 14.7 lbf/in 2, and some NO is formed. At what temperature will the mole fraction of NO be 0.001?
The combustion products from burning pentane, C5H12 with pure oxygen in a stoichiometric ratio exists at 4400 R. Consider the dissociation of only CO2 and find the equilibrium mole fraction of CO.
A gas mixture of 1 pound mol carbon monoxide, 1 pound mol nitrogen, and 1 pound mol oxygen at 77 F, 20 lbf/in 2, is heated in a constant pressure SSSF process. The exit mixture can be assumed to be in chemical equilibrium with CO2, CO, O2, and N2 present. The mole fraction of CO2 at this point is
In a test of a gas-turbine combustor, saturated-liquid methane at 210 R is to be burned with excess air to hold the adiabatic flame temperature to 2880 R. It is assumed that the products consist of a mixture of CO2, H2O, N2, O2, and NO in chemical equilibrium. Determine the percent excess air used
Acetylene gas at 77 F is burned with 140% theoretical air, which enters the burner at 77 F, 14.7 lbf/in 2, 80% relative humidity. The combustion products form a mixture of CO2, H2O, N2, O2, and NO in chemical equilibrium at 3500 F, 14.7 lbf/in 2. This mixture is then cooled to 1340 F very rapidly,
The equilibrium reaction with methane as CH4 C + 2H2 has ln K = -0.3362 at 1440 R and ln K = -4.607 at 1080 R. By noting the relation of K to temperature, show how you would interpolate ink in (1/T) to find K at 1260 R and compare that to a linear interpolation.
Use the information in problem 15.67 to estimate the enthalpy of reaction, Ho, at 1260 R using the van’t Hoff equation (see problem 15.28) with finite differences for the derivatives.
An important step in the manufacture of chemical fertilizer is the production of ammonia, according to the reaction: N2 + 3H2 2NH3 a. Calculate the equilibrium constant for this reaction at 300 F. b. For an initial composition of 25% nitrogen, 75% hydrogen, on a mole basis
Ethane is burned with 150% theoretical air in a gas turbine combustor. The products exiting consist of a mixture of CO2, H2O, O2, N2, and NO in chemical equilibrium at 2800 F, 150 lbf/in 2. Determine the mole fraction of NO in the products. Is it reasonable to ignore CO in the products?
One pound mole of air (assumed to be 78% nitrogen, 21% oxygen, and 1% argon) at room temperature is heated to 7200 R, 30 lbf/in 2. Find the equilibrium composition at this state, assuming that only N2, O2, NO, O, and Ar are present.
Dry air is heated from 77 F to 7200 R in a 14.7 lbf/in 2 constant-pressure process. List the possible reactions that may take place and determine the equilibrium composition. Find the required heat transfer.
Acetylene gas and x times’ theoretical air (x 1) at room temperature and 75 lbf/in 2 are burned at constant pressure in an adiabatic SSSF process. The flame temperature is 4600 R, and the combustion products are assumed to consist of N2, O2, CO2, H2O, CO, and NO. Determine the
One pound mole of water vapor at 14.7 lbf/in 2, 720 R, is heated to 5400 R in a constant pressure SSSF process. Determine the final composition, assuming that H2O, H2, H, O2, and OH are present at equilibrium.
Methane is burned with theoretical oxygen in an SSSF process, and the products exit the combustion chamber at 5300 F, 100 lbf/in 2. Calculate the equilibrium composition at this state, assuming that only CO2, CO, H2O, H2, O2, and OH are present. Combustion: CH4 + 2 O2 CO2 + 2 H2O
Steam leaves a nozzle with a pressure of 500 kPa, a temperature of 350C, and a velocity of 250 m/s. What is the isentropic stagnation pressure and temperature?
An object from space enters the earth’s upper atmosphere at 5 kPa, 100 K with a relative velocity of 2000 m/s or more. Estimate the object’s surface temperature.
The products of combustion of a jet engine leave the engine with a velocity relative to the plane of 400 m/s, a temperature of 480C, and a pressure of 75 kPa. Assuming that k 1.32, Cp 1.15 kJ/kg K for the products, determine the stagnation pressure and
A meteorite melts and burn up at temperatures of 3000 K. If it hits air at 5 kPa, 50 K how high a velocity should it has to experience such a temperature?
I drive down the highway at 110 km/h on a day with 25C, 101.3 kPa. I put my hand, cross sectional area 0.01 m2, flat out the window. What is the force on my hand and what temperature do I feel?
Air leaves a compressor in a pipe with a stagnation temperature and pressure of 150C, 300 kPa, and a velocity of 125 m/s. The pipe has a cross-sectional area of 0.02 m2. Determine the static temperature and pressure and the mass flow rate.
A stagnation pressure of 108 kPa is measured for an air flow where the pressure is 100 kPa and 20C in the approach flow. What is the incoming velocity?
A jet engine receives a flow of 150 m/s air at 75 kPa, 5C across an area of 0.6 m2 with an exit flow at 450 m/s, 75 kPa, 600 K. Find the mass flow rate and thrust.
A water cannon sprays 1 kg/s liquid water at a velocity of 100 m/s horizontally out from a nozzle. It is driven by a pump that receives the water from a tank at 15C, 100 kPa. Neglect elevation differences and the kinetic energy of the water flow in the pump and hose to the nozzle. Find the
An irrigation pump takes water from a lake and discharges it through a nozzle. At the pump exit the pressure is 700 kPa, and the temperature is 20C. The nozzle is located 10 m above the pump and the atmospheric pressure is 100 kPa. Assuming reversible flow through the system determine the
A water turbine using nozzles is located at the bottom of Hoover Dam 175 m below the surface of Lake Mead. The water enters the nozzles at a stagnation pressure corresponding to the column of water above it minus 20% due to friction. The temperature is 15C and the water leaves at standard
A water tower on a farm holds 1 m3 liquid water at 20C, 100 kPa in a tank on top of a 5 m tall tower, A pipe leads to the ground level with a tap that can open a 1.5 cm diameter hole. Neglect friction and pipe losses and estimate the time it will take to empty the tank for water.
Find the speed of sound for air at 100 kPa at the two temperatures 0C and 30C. Repeat the answer for carbon dioxide and argon gases.
If the sound of thunder is heard 5 seconds after seing the lightning and the weather is 20C how far away is the lightning taking place?
Estimate the speed of sound for steam directly from Eq. 16.28 and the steam tables for a state of 6 MPa, 400C. Use table values at 5 and 7 MPa at the same entropy as the wanted state. Eq. 16.28 is then done by finite difference. Find also the answer for the speed of sound assuming steam is
A convergent-divergent nozzle has a throat diameter of 0.05 m and an exit diameter of 0.1 m. The inlet stagnation state is 500 kPa, 500 K. Find the back pressure that will lead to the maximum possible flow rate and the mass flow rate for three different gases as: air; hydrogen or carbon dioxide.
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