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physics
thermodynamics

Fundamentals of Thermodynamics 6th edition Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen - Solutions

What is the dew point of hydrogen burned with stoichiometric pure oxygen? air?
Liquid nitromethane is added to the air in a carburetor to make a stoichiometric mixture where both fuel and air are added at 298 K, 100 kPa. After combustion a constant pressure heat exchanger brings the products to 600 K before being exhausted. Assume the nitrogen in the fuel becomes N2 gas. Find
Hydrogen gas is burned with pure oxygen in a steady flow burner where both reactants are supplied in a stoichiometric ratio at the reference pressure and temperature. What is the adiabatic flame temperature?
In a rocket, hydrogen is burned with air, both reactants supplied as gases at Po, To. The combustion is adiabatic and the mixture is stoichiometeric (100% theoretical air). Find the products dew point and the adiabatic flame temperature (~2500 K).
Carbon is burned with air in a furnace with 150% theoretical air and both reactants are supplied at the reference pressure and temperature. What is the adiabatic flame temperature?
A stoichiometric mixture of benzene, C6H6, and air is mixed from the reactants flowing at 25°C,100 kPa. Find the adiabatic flame temperature. What is the error if constant specific heat at T0 for the products from Table A.5 are used?
Hydrogen gas is burned with 200% theoretical air in a steady flow burner where both reactants are supplied at the reference pressure and temperature. What is the adiabatic flame temperature?
A gasturbine burns natural gas (assume methane) where the air is supplied to the combustor at 1000 kPa, 500 K and the fuel is at 298 K, 1000 kPa. What is the equivalence ratio and the percent theoretical air if the adiabatic flame temperature should be limited to 1800 K?
Liquid n-butane at T0, is sprayed into a gas turbine with primary air flowing at 1.0 MPa, 400 K in a stoichiometric ratio. After complete combustion, the products are at the adiabatic flame temperature, which is too high, so secondary air at 1.0 MPa, 400 K is added, with the resulting mixture being
Butane gas at 25°C is mixed with 150% theoretical air at 600 K and is burned in an adiabatic steady flow combustor. What is the temperature of the products exiting the combustor?
Natural gas, we assume methane, is burned with 200% theoretical air and the reactants are supplied as gases at the reference temperature and pressure. The products are flowing through a heat exchanger and then out the exhaust, as in Fig. P14.79. What is the adiabatic flame temperature right after
How does the dew point change as equivalence ratio goes from 0.9 to 1 to 1.1?
Liquid butane at 25oC is mixed with 150% theoretical air at 600 K and is burned in a steady flow burner. Use the enthalpy of combustion from Table 14.3 to find the adiabatic flame temperature out of the burner.
Acetylene gas at 25°C, 100 kPa is fed to the head of a cutting torch. Calculate the adiabatic flame temperature if the acetylene is burned with a. 100% theoretical air at 25°C. b. 100% theoretical oxygen at 25°C.
Ethene, C2H4, burns with 150% theoretical air in a steady flow constant-pressure process with reactants entering at P0, T0. Find the adiabatic flame temperature. Stoichiometric
Solid carbon is burned with stoichiometric air in a steady flow process. The reactants at T0, P0 are heated in a preheater to T2 = 500 K as shown in Fig. P14.83, with the energy given by the product gases before flowing to a second heat exchanger, which they leave at T0. Find the temperature of the
Gaseous ethanol, C2H5OH, is burned with pure oxygen in a constant volume combustion bomb. The reactants are charged in a stoichiometric ratio at the reference condition. Assume no heat transfer and find the final temperature ( > 5000 K).
The enthalpy of formation of magnesium oxide, MgO(s), is −601827 kJ/kmol at 25°C. The melting point of magnesium oxide is approximately 3000 K, and the increase in enthalpy between 298 and 3000 K is 128 449 kJ/kmol. The enthalpy of sublimation at 3000 K is estimated at 418 000 kJ/kmol, and the
Calculate the irreversibility for the process described in Problem 14.41. In Problem 14.41. A rigid vessel initially contains 2 kmol of carbon and 2 kmol of oxygen at 25°C, 200 kPa. Combustion occurs, and the resulting products consist of 1 kmol of carbon dioxide, 1 kmol of carbon monoxide, and
Methane is burned with air, both of which are supplied at the reference conditions. There is enough excess air to give a flame temperature of 1800 K. What are the percent theoretical air and the irreversibility in the process?
Consider the combustion of hydrogen with pure oxygen in a stoichiometric ratio under steady flow adiabatic conditions. The reactants enter separately at 298 K, 100 kPa and the product(s) exit at a pressure of 100 kPa. What is the exit temperature and what is the irreversibility?
Pentane gas at 25°C, 150 kPa enters an insulated steady flow combustion chamber. Sufficient excess air to hold the combustion products temperature to 1800 K enters separately at 500 K, 150 kPa. Calculate the percent theoretical air required and the irreversibility of the process per kmol of
In most cases combustion products are exhausted above the dew point. Why?
Consider the combustion of methanol, CH3OH, with 25% excess air. The combustion products are passed through a heat exchanger and exit at 200 kPa, 400 K. Calculate the absolute entropy of the products exiting the heat exchanger assuming all the water is vapor.
Consider the combustion of methanol, CH3OH, with 25% excess air. The combustion products are passed through a heat exchanger and exit at 200 kPa, 40°C. Calculate the absolute entropy of the products exiting the heat exchanger per kilomole of methanol burned, using the proper amounts of liquid and
An inventor claims to have built a device that will take 0.001 kg/s of water from the faucet at 10°C, 100 kPa, and produce separate streams of hydrogen and oxygen gas, each at 400 K, 175 kPa. It is stated that this device operates in a 25°C room on 10-kW electrical power input. How do you
Two kilomoles of ammonia are burned in a steady flow process with x kmol of oxygen. The products, consisting of H2O, N2, and the excess O2, exit at 200°C, 7 MPa. a. Calculate x if half the water in the products is condensed. b. Calculate the absolute entropy of the products at the exit conditions.
Graphite, C, at P0, T0 is burned with air coming in at P0, 500 K in a ratio so the products exit at P0, 1200 K. Find the equivalence ratio, the percent theoretical air, and the total irreversibility.
A flow of hydrogen gas is mixed with a flow of oxygen in a stoichiometric ratio, both at 298 K and 50 kPa. The mixture burns without any heat transfer in complete combustion. Find the adiabatic flame temperature and the amount of entropy generated per kmole hydrogen in the process.
A closed rigid container is charged with propene, C3H6, and 150% theoretical air at 100 kPa, 298 K. The mixture is ignited and burns with complete combustion. Heat is transferred to a reservoir at 500 K so the final temperature of the products is 700 K. Find the final pressure, the heat transfer
Repeat Problem 14.42, but assume that saturated-liquid oxygen at 90 K is used instead of 25°C oxygen gas in the combustion process. Use the generalized charts to determine the properties of liquid oxygen.
Hydrogen peroxide, H2O2, enters a gas generator at 25°C, 500 kPa at the rate of 0.1 kg/s and is decomposed to steam and oxygen exiting at 800 K, 500 kPa. The resulting mixture is expanded through a turbine to atmospheric pressure, 100 kPa, as shown in Fig. P14.98. Determine the power output of the
Liquid butane at 25°C is mixed with 150% theoretical air at 600 K and is burned in an adiabatic steady state combustor. Use the generalized charts for the liquid fuel and find the temperature of the products exiting the combustor.
Is the concept of equilibrium limited to thermodynamics?
For a mixture of O2 and O I add some argon keeping constant T, P; what happens to the moles of O?
If I consider the non-frozen (composition can vary) heat capacity, but still assume all components are ideal gases, does that C become a function of temperature? of pressure?
What is K for the water gas reaction in Example 15.4 at 1200 K?
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 40°C. 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 30oC. The pressure at the top of the well is 14 MPa, and the composition on a mole basis is 90% methane, 10% ethane. Each component is in equilibrium (top to bottom) with dG + g dZ = 0 and
A container has liquid water at 20oC, 100 kPa in equilibrium with a mixture of water vapor and dry air also at 20oC, 100 kPa. How much is the water vapor pressure and what is the saturated water vapor pressure?
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, βT. For liquid water at 20oC, βT = 0.0005 [1/MPa]. Use the result of the first question to estimate the
Calculate the equilibrium constant for the reaction O2 ⇔ 2O at temperatures of 298 K and 6000 K. Verify the result with Table A.11.
For the dissociation of oxygen, O2 ⇔ 2O, around 2000 K we want a mathematical expression for the equilibrium constant K(T). Assume constant heat capacity, at 2000 K, for O2 and O from Table A.9 and develop the expression from Eqs. 15.12 and 15.15.
Calculate the equilibrium constant for the reaction H2 ⇔ 2H at a temperature of 2000 K, using properties from Table A.9. Compare the result with the value listed in Table A.11.
Plot to scale the values of ln K versus 1/T for the reaction 2 CO2 ⇔ 2 CO + O2.
Calculate the equilibrium constant for the reaction: 2CO2 ⇔ 2CO + O2 at 3000 K using values from Table A.9 and compare the result to Table A.11.
How is a chemical equilibrium process different from a combustion process?
Consider the dissociation of oxygen, O2 ⇔ 2 O, starting with 1 kmol oxygen at 298 K and heating it at constant pressure 100 kPa. At which temperature will we reach a concentration of monatomic oxygen of 10%?
Pure oxygen is heated from 25°C to 3200 K in an steady flow process at a constant pressure of 200 kPa. Find the exit 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.
One kilomole Ar and one kilomole O2 are 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.
Consider the reaction 2 CO2 ⇔ 2 CO + O2 obtained after heating 1 kmol CO2 to 3000 K. Find the equilibrium constant from the shift in Gibbs function and verify its value with the entry in Table A.11. What is the mole fraction of CO at 3000 K, 100 kPa?
Air (assumed to be 79% nitrogen and 21% oxygen) is heated in a steady state 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?
The combustion products from burning pentane, C5H12, with pure oxygen in a stoichiometric ratio exists 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.11 to answer which of the nitrogen oxides, NO or NO2, is the more stable at ambient conditions? What about at 2000 K?
Pure oxygen is heated from 25°C, 100 kPa to 3200 K in a constant volume container. Find the final pressure, composition, and the heat transfer.
A mixture of 1 kmol carbon dioxide, 2 kmol carbon monoxide, and 2 kmol oxygen, at 25°C, 150 kPa, is heated in a constant pressure steady state 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 2 kmol of nitrogen, which does not dissociate during the process.
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 and determine the equilibrium constant for this reaction at a temperature
Consider combustion of methane with pure oxygen forming carbon dioxide and water as the products. Find the equilibrium constant for the reaction at 1000 K. Use an average heat capacity of Cp = 52 kJ/kmol K for the fuel and Table A.9 for the other components.
Find the equilibrium constant for the reaction: 2NO + O2 ⇔ 2NO2 from the elementary reaction in Table A.11 to answer these two questions. Which of the nitrogen oxides NO or NO2 is the more stable at 25oC, 100 kPa? At what T do we have an equal amount of each?
The equilibrium reaction as: CH4 ⇔ C + 2H2. has ln K = -0.3362 at 800 K and lnK = -4.607 at 600 K. By noting the relation of K to temperature show how you would interpolate ln K in (1/T) to find K at 700 K and compare that to a linear interpolation.
Water from the combustion of hydrogen and pure oxygen is at 3800 K and 50 kPa. Assume we only have H2O, O2 and H2 as gases find the equilibrium composition.
Complete combustion of hydrogen and pure oxygen in a stoichiometric ratio at PoTo to form water would result in a computed adiabatic flame temperature of 4990 K for a steady state setup. a. How should the adiabatic flame temperature be found if the equilibrium reaction 2H2 + O2 ⇔ 2 H2O is
The van't Hoff equationrelates the chemical equilibrium constant K to the enthalpy of reaction Î”Ho. From the value of K in Table A.11 for the dissociation of hydrogen at 2000 K and the value of Î”Ho calculated from Table A.9 at 2000 K use van€™t Hoff equation to
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
Consider the water gas reaction in Example 15.4. Find the equilibrium constant at 500, 1000, 1200 and 1400 K. What can you infer from the result?
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
A piston/cylinder contains 0.1 kmol hydrogen and 0.1 kmol Ar gas at 25°C, 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.
A tank contains 0.1 kmol hydrogen and 0.1 kmol of argon gas at 25oC, 200 kPa and the tank keeps constant volume. To what T should it be heated to have a mole fraction of atomic hydrogen, H, of 10%?
A gas mixture of 1 kmol carbon monoxide, 1 kmol nitrogen, and 1 kmol oxygen at 25°C, 150 kPa, is heated in a constant pressure 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 0.176. Calculate the
A rigid container initially contains 2 kmol of carbon monoxide and 2 kmol of oxygen at 25°C, 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 composition
A coal gasifier produces a mixture of 1 CO and 2H2 that is fed to a catalytic converter to produce methane. The reaction is CO + 3H2 ⇔ CH4 + H2O. The equilibrium constant at 600 K is K = 1.83 × 106. What is the composition of the exit flow assuming a pressure of 600 kPa?
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 reaction CH4 + H2O ⇔ CO + 3H2. One kilomole each of methane and water are fed to a
Use the information in Problem 15.45 to estimate the enthalpy of reaction, ΔHo, at 700 K using Van’t Hoff equation (see problem 15.48) with finite differences for the derivatives.
Acetylene gas at 25°C is burned with 140% theoretical air, which enters the burner at 25°C, 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 rapidly, so that
In a steady flow burner T is not controlled, which properties are?
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 25°C, 5 MPa, and 2 kmol of steam at 300°C, 5 MPa, enter a catalytic reactor. An ideal gas mixture of ethanol, ethylene, and water
Methane at 25°C, 100 kPa, is burned with 200% theoretical oxygen at 400 K, 100 kPa, in an adiabatic steady state 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. Previous problem. Methane at 25°C, 100 kPa, is burned with 200% theoretical oxygen at 400 K, 100 kPa, in an adiabatic steady state process, and the products of combustion exit at 100 kPa. Assume
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 150°C. b. For an initial composition of 25% nitrogen, 75% hydrogen, on a mole basis, calculate the
One kilomole 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 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
Hydrides are rare earth metals, M, that have the ability to react with hydrogen to form a different substance MHx with a release of energy. The hydrogen can then be released, the reaction reversed, by heat addition to the MHx. In this reaction only the hydrogen is a gas so the formula developed for
Water from the combustion of hydrogen and pure oxygen is at 3800 K and 50 kPa. Assume we only have H2O, O2, OH and H2 as gases with the two simple water dissociation reactions active find the equilibrium composition.
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?
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.
In a closed rigid combustion bomb which properties are held fixed?
A mixture of 1 kmol water and 1 kmol oxygen at 400 K is heated to 3000 K, 200 kPa, in a steady flow process. Determine the equilibrium composition at the outlet of the heat exchanger, assuming that the mixture consists of H2O, H2, O2, and OH.
One kilomole 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.
One kilomole of water vapor at 100 kPa, 400 K, is heated to 3000 K in a constant pressure steady flow process. Determine the final composition, assuming that H2 O, H2 , H, O2, and OH are present at equilibrium.
Acetylene gas and x times theoretical air (x > 1) at room temperature and 500 kPa are burned at constant pressure in an adiabatic steady flow 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.
At 10 000 K the ionization reaction for Ar is: Ar ⇔ Ar+ + e− with equilibrium constant of K = 4.2 × 10−4. What should the pressure be for a mole concentration of argon ions (Ar+) of 10%?
Operation of an MHD converter requires an electrically conducting gas. It is proposed to use helium gas €œseeded€ with 1.0 mole percent cesium, as shown in Fig. P15.75. The cesium is partly ionized
One kilomole 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 eˆ’ according to the simultaneous reactionsThe ionization equilibrium constants for these reactions at 20000 K have been
At 10 000 K the two ionization reactions for N and Ar ashave equilibrium constants of K1 = 4.2 Ã— 10ˆ’4 and K2 = 6.3 Ã— 10ˆ’4, respectively. If we start out with 1 kmol Ar and 0.5 kmol N2, what is the equilibrium composition at a pressure of 10 kPa?
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 eˆ’ are present. For the ionization reaction N ‡” N+ eˆ’, the ionization equilibrium constant K has been calculated from spectroscopic data as
Repeat Problem 15.21 using the generalized charts, instead of ideal gas behavior. Problem 15.21 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 40°C. What
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

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