Questions and Answers of Introductory Chemical Engineering Thermodynamics

A feed stream containing a mixture of 40% n-butane, 30% n-pentane, and 30% n-hexane fl ows into a fl ash unit. The fl ash temperature is 290 K and the fl ash pressure is 0.6 bar. What is the ratio of
Calculate the liquid and vapor compositions of butane(a) and n-hexane(b) at 0°C and 0.5 bar. You may assume the liquid forms an ideal solution.
Calculate the liquid and vapor compositions of n-pentane(a) and benzene(b) at 16°C and 0.333 bar. The excess Gibbs energy can be described by the two-suffi x Margules equation with A = 1816
Calculate the liquid and vapor compositions of a binary mixture of isobutane (a) and hydrogen sulfi de (b) at 4.5°C and 8.77 bar. The excess Gibbs energy can be described by the three-suffi x
At 60°C, ethanol (1) and ethyl acetate (2) exhibit an azeotrope at a pressure of 0.64 bar and x1 = 0.4.(a) You wish to use the two-suffi x Margules equation as a model for gE. From these data,
Consider a binary mixture of n-propanol and water in vapor–liquid equilibrium (VLE). Let n-propanol be designated species 1 and water, species 2. A plot of the activity coeffi cients for this
An equimolar liquid phase of benzene (1) and m-xylene (2) coexists with its vapor at 260°C.At this temperature, the saturation pressures are Using the van der Waals equation of state, calculate the
Consider a mixture of 1-propanol(a) and water(b) in vapor–liquid equilibrium at 25°C. For a liquid with mole fraction xa 5 0.2, answer the following questions. The three-suffi x Margules
Example 8.6 illustrates how you solve a dew-point calculation for a binary mixture of a nonideal liquid and a nonideal gas with T known. This problem corresponds to quadrant I in Figure 8.2.Develop
A binary mixture of water (1) and benzene (2) is in vapor–liquid equilibrium at a liquid mole fraction x1 = 0.6 and a pressure of 74.5 kPa. The liquid phase nonideality can be described by the
Consider a mixture of 1-propanol(a) and water (b). At 25°C, the three-suffi x Margules equation parameters are:Does this binary mixture form an azeotrope at 25°C? If so, at what pressure does the
At 20°C and 0.073 bar, a binary liquid mixture of cyclohexane (1) and toluene (2) is in vapor–liquid equilibrium. The liquid mole fraction of cyclohexane is measured to be x1 = 0.471. Assume that
Consider the system of ethanol (1)–benzene (2) at 25°C. This mixture exhibits an azeotrope at a mole fraction of x1 5 0.28 and a pressure of 122.3 torr. Determine values for the parameters in the
Consider a mixture of species 1 and 2 in vapor–liquid equilibrium at 25°C and 90 bar. The following equation of state is available for the vapor phase:and y1 and y2 are the mole fractions of
A mixture of methanol(a) and ethyl acetate(b) exhibits an azeotrope at 55°C. Their saturation pressures are 68.8 and 46.5 kPa, respectively. The liquid-phase nonideality can be described by the
Consider a mixture of benzene (1) and a proprietary organic molecule (2) that is in vapor–liquid equilibrium at 70°C. The proprietary molecule and benzene form a completely miscible liquid phase,
mixture of toluene (1) and polystyrene (2) is placed in an evacuated closed container (there is no air in the container). The container is then brought to 20.57 bar and 301°C where the liquid
The following data are reported for a binary mixture of species 1 and 2 at 40°C. The activity coeffi cients at infi nite dilution are:Answer the following questions:(a) 4 moles of species 1 and 6
A binary mixture of components a and b contains 1 mol a and 3 mol b in the liquid phase at 25°C and 0.50 bar. The excess Gibbs energy of the liquid mixture can be described by the van Laar equation
The following plot shows a Pxy phase diagram for a binary mixture of species 1 and 2 at 300 K.Answer the following:(a) A mixture of 2 mol of species 1 and 1 mol of species 2 exists at 20 kPa.
At 90°C, a binary-mixture of n-propanol(a) and water(b) follows the van Laar equation with A = 7,850 [J/mol] and B = 3,410 [J/mol].(a) Consider a liquid with 60 mole% n-propanol at 90°C in
A vapor–liquid phase diagram for a binary mixture of species 1 and 2 at 293 K is shown in the following fi gure.Answer the following questions.(a) At 293 K, what is the value of
Consider a binary system of water vapor (1) in air (2) initially at room temperature and pressure (such as the air in this room). You desire to compress the gas to 100 bar and then cool it to 210 °C
The Pxy phase diagram for a binary mixture of species “1” and “2” at 300 K is shown in the following fi gure.Answer the following questions:(a) On the g raph, identify the single-phase vapor
The Henry’s law constant and an expression for the activity coeffi cient have been found for the solute for a binary mixture of species 1 (solute)–2 (solvent) at 20°C. and, H = 0.5[Pa] Henry's=
What is the solubility of oxygen in methanol at 25°C and 1 bar? What is the solubility of oxygen in methanol at 25°C and 100 bar? Take Vo = 4.5 10-5 [m/mol].
A binary mixture of carbon dioxide and water exists in vapor–liquid equilibrium at 343.15 K and 1 bar. The solubility of CO2 in the liquid has been measured as xCO2 = 0.000255.What is the Henry’s
The following data are available for the Henry’s law constant of N2 in H2O at 19.4°C. From these data, estimate 00: 8 N*
The following data are available for the Henry’s law constant of O2 in benzene. From these data, estimate Ho, - ho:
Develop a computer spreadsheet or write a program to verify that the objective functionin Example 8.9 gives the value A = 1399 [J/mol]. What value do you obtain for OFgE?Example 8.9 2 OF i i = (g GE
Develop a computer spreadsheet or write a program to verify that the objective functionin Example 8.9 gives the value A = 1424 [J/mol]. What value do you obtain for OFγ? "HO = calc [((y yale) /7) +
Liquid–vapor equilibrium data have been collected for a binary system of benzene (1)–cyclohexane (2) at 60°C. Mole fraction of liquid and vapor vs. total pressure are reported in the table
Liquid–vapor equilibrium data have been collected for a binary system of methanol (1)–water (2) at 40°C. Mole fraction of liquid vs. total pressure are reported in the table below. Develop a
Test the liquid–vapor equilibrium data for the binary system of methanol (1)–water (2) at 40°C presented in Problem 8.53 for thermodynamic consistency by using the area test.Problem
The following vapor–liquid equilibrium data have been reported for a binary mixture of acetone (1) in chloroform (2) at 35. 17°C. Test these data for thermodynamic consistency. X1 0 0.0821 0.1953
The following vapor–liquid equilibrium data have been reported for a binary mixture of acetone (1) in water (2) at 1 atm. Test these data for thermodynamic consistency. X1 0 0.015 0.036 0.074 0.175
You wish to fi t the benzene (1)–isooctane (2) system to the following model for gE:The system temperature of interest is 200°C. After a literature search, the only vapor–liquid equilibrium data
Using the Peng–Robinson equation of state, calculate the saturation pressure of pure n- pentane at 400 K using fugacity coeffi cients to calculate the fugacity for both vapor and liquid phases.
Using the Peng–Robinson equation of state, calculate the saturation pressure of pure propane at 0°C using fugacity coeffi cients to calculate the fugacity for both vapor and liquid phases.Compare
Using the Peng–Robinson equation of state, calculate the saturation pressure of pure benzene at 400 K using fugacity coeffi cients to calculate the fugacity for both vapor and liquid phases.
Using the equation of state method, determine the equilibrium composition in the vapor phase and the system pressure of a mixture of methane (1) and n-pentane (2) with a liquid mole fraction of x1 =
Repeat Problem 8.61 using the Peng–Robinson equation of state. Use a value for the binary interaction parameter of 0.026.Problem 8.61Using the equation of state method, determine the equilibrium
Using the equation of state method, determine the equilibrium composition in the vapor phase and the system pressure of a mixture of carbon dioxide (1) and benzene (2) with a liquid mole fraction of
Repeat Problem 8.63 using the Peng–Robinson equation of state. Use a value for the binary interaction parameter of 0.077.Problem 8.63Using the equation of state method, determine the equilibrium
Repeat Problem 8.67 using the Peng–Robinson equation of state. Use a value for the binary interaction parameter of:(a) 0(b) 0.077Problem 8.67Using the equation of state method, construct a Pxy
Using the equation of state method, construct a Pxy diagram for a binary mixture of carbon dioxide (1) and benzene (2) at 100°C. Use the van der Waals equation of state to determine fugacity for
Using the equation of state method, construct a Pxy diagram for a binary mixture of carbon dioxide (1) and benzene (2) at 25°C. Use the van der Waals equation of state to determine fugacity for both
At a 300 K and 1 bar, a binary mixture of species a and b form two partially miscible liquid phases. The following activity coeffi cients at infi nite dilution are reported: Using the three-suffi x
Consider a binary liquid mixture of hexane (1) and acetone (2). At 15°C and 300 bar, this mixture forms two partially miscible liquid phases. Phase α has 20 total moles with x1α = 0.2, while phase
At 25°C and 1 bar, the following composition has been reported for a liquid–liquid mixture of CHCl3(a) and H2O(b) : xα α = 0.987 and xαβ = 0.0013. From these data predict the three-suffi x
The Wilson equation requires positive values for binary parameters Lab and Lba. Verify that this activity coeffi cient model is incapable of describing the instability of partially miscible liquids.
Tetrahydrofuran(a) and water(b) separate into two liquid phases at 1 bar and 50°C. Determine the composition of each liquid phase. The following three-suffi x Margules parameters have been
Tetrahydrofuran(a) and water(b) separate into two liquid phases at 1 bar and 50°C. Determine the composition range over which the system is inherently unstable and will spontaneously separate into
The mole fraction of isobutane in a liquid–liquid mixture of isobutane(a) in equilibrium with furfural(b) at 64°C and 10 bar has been measured to be:
A binary mixture of species a and b are in liquid–liquid equilibrium at 25°C. This mixture can be described by the two-suffi x Margules equation with A = 7,300 [J/mol]. Assume A does not change
A binary mixture of species a and b is in liquid–liquid–vapor equilibrium at 25°C. The liquid compositions are xαa = 0.92 and xβa = 0.08, and the saturation pressures of a and b are Psat a =
A binary mixture of water(a) and 1-butanol(b) exhibits vapor–liquid–liquid equilibrium at 25°C. The activity coeffi cients at infi nite dilution are given by Determine the composition of the
A set of mixing processes is shown in the following fi gures. The volumes are represented by the size of the boxes. For each process, determine whether Ds is greater than zero, less than zero, or
State the conditions under which the following equations apply. Be as specifi c as you can with the limitations. (a) q = [Tds (b) h h = cp(Ta - T) (c) Asumie > 0 (d) ASUT (e) Asunto 2 Courr 1 Tur QH
Consider two ideal gases, A and B, that are initially separated. For each of the following processes, the gases are allowed to mix. Determine if the entropy change of the system is positive,
Consider an ideal gas. For each of the following processes, determine if the entropy change of the system is positive, negative, zero, or you cannot tell. Explain.(a) Isothermal
Consider the following processes and determine if the entropy change of the system is positive, negative, zero, or you cannot tell. Explain.(a) Liquid water is frozen to form ice.(b) 1 mol of
Consider an ideal gas that undergoes two alternative processes from state 1 to state 2. The path for the fi rst process (Path 1) is reversible, and the path of the second process (Path 2) is
A black box is bolted to a beam with a cable as shown in the following fi gure. Consider the box as the system. During the process, the box raises in height as the cable goes into the box by an
In Problem 2.12, you explained why a thick rubber band heats when stretched. Offer an alternative explanation in the context of entropy. You may consider this process isentropic.Problem 2.12I
Qualitatively sketch the Ts diagram corresponding to the real Rankine cycle given in Example 3.15.Example 3.15 EXAMPLE 3.15 Redo the analysis of the Rankine cycle of Example 3.14 but include
Ts diagrams for two reversible thermodynamic power cycles are shown in the following fi gure.Both cycles operate between a high temperature reservoir at 500 K and a low temperature reservoir at 300
Ts diagrams for two reversible thermodynamic power cycles are shown in the following fi gure.Both cycles operate between a high temperature reservoir at 500 K and a low temperature reservoir at 300
CdTe forms a II–VI compound semiconductor. This solid forms a well-ordered single crystal where Cd atoms and Te atoms sit in distinct sites adjacent to each other in a crystal lattice. Estimate the
In the 1959 Rede Lecture, The Two Cultures, C. P. Snow asserts:A good many times I have been present at gatherings of people who, by the standards of traditional culture, are thought highly educated
In his book The Trouble Waters, Henry Morris proclaims:The Law of Increasing Entropy is an impenetrable barrier which no evolutionary mechanism yet suggested has ever been able to overcome. Evolution
“Four of a kind” is one of the best hands you can have in poker. Can you relate this statement to the concept of entropy? Would you say this hand has a high value of s?
The concept of entropy was developed in the nineteenth century, in order to study the efficiency of the steam engine, largely through the work of Sadi Carnot, Rudolph Clausius, and Lord Kelvin.
Develop a general expression for Δssys for an ideal gas that goes from (v1, T1) to (v2, T2) based on the path below. S Volume (m/mol) NT State 1 (T.V) Real path T Step 1 ASreal AShypothetical
Develop a general expression for Dssys for an ideal gas that goes from (P1, T1) to (P2, T2) where heat capacity is given by: Cp = A + BT + CT2
A rigid vessel contains 10 kg of steam. The steam is initially at 10 bar and 300°C. After a period of time, the pressure in the vessel is reduced to 1 bar due to heat transfer with the surroundings.
A 10-kg block of copper is initially at 100°C. It is thrown in a very large lake that is at 280 K.What is the entropy change of the copper? What is the entropy change of the universe?
Calculate the change in entropy for the system for each of the following cases. Explain the sign that you obtain by a physical argument.(a) A gas undergoes a reversible, adiabatic expansion from an
Calculate the change in entropy of the universe for the process described in Problem 2.28.Repeat for Problem 2.29.Problem 2.28 Consider a piston–cylinder assembly that contains 1 mole of ideal
Determine the change in entropy of an ideal gas with constant heat capacity, cP = (7/2)R, between the following states: (a) P = 1 bar, T = 300 K; P = 0.5 bar, T = 500 K (b) v = 0.05 m/mol, T = 300 K;
Compare the change in entropy(a) when water is heated from its freezing point to its boiling point at 1 atm and(b) when saturated liquid water is vaporized at 1 atm.
You have just cooled a glass of tap water at 20°C by adding ice, at 210°C. The glass originally contains 400 mL of tap water, to which 100 g of ice is added. Assume that the glass is
Consider a piston–cylinder assembly that initially contains 0.5 kg of steam at 400°C and 100 bar. For the isothermal expansion of the steam in this system to a fi nal pressure of 1 bar, determine
Consider the piston–cylinder assembly shown at the top of page. It is well insulated and initially contains two 5000-kg blocks at rest on the 0.05-m2 piston. The initial temperature is 500 K.The
Problem 3.27 consists of an irreversible process in which an ideal gas with constant heat capacity was compressed in a piston–cylinder assembly. As part of this problem, you were asked to calculate
Consider a well-insulated piston–cylinder assembly. O2, initially at 250 K and 1 bar, undergoes a reversible compression to 12.06 bar. You may assume oxygen is an ideal gas. Answer the following
The insulated vessel shown below has two compartments separated by a membrane. On one side is 1 kg of steam at 400°C and 200 bar. The other side is evacuated. The membrane ruptures, fi lling the
A partition divides a rigid, well-insulated 1-m3 tank into two equal parts. The left side contains an ideal gas [cP = (5/2)R] at 10 bar and 300 K. The right side contains nothing; it is a vacuum.A
An insulated tank is divided by a thin partition.(a) On the left is 0.79 mole of N2 at 1 bar and 298 K; on the right is 0.21 mole of O2 at 1 bar and 298 K. The partition ruptures. What is ΔSuniv
Consider the well-insulated, rigid container shown in the following fi gure. Two compartments, A and B, contain H2O and are separated by a thin metallic piston. Side A is 50 cm long. Side B is 10 cm
Consider the well-insulated container shown below. Two gases, gas A and gas B, are separated by a metallic piston. The piston is initially held in place by a latch 10 cm from the left of the
Steam at 8 MPa and 500°C fl ows through a throttling device, where it exits at 100 kPa.Determine the entropy change for this process.
A fast-talking salesperson comes to your doorstep and says she is down on her luck and is willing to sell you the patent rights to her most glorious invention. She brings out a mysterious black box
Steam enters a nozzle at 4 MPa and 640°C with a velocity of 20 m/s. This process may be considered reversible and adiabatic. The nozzle exit pressure is 0.1 MPa.(a) Draw a sketch of this process.
Propane at 350°C and 600 cm3/mol is expanded in a turbine. The exhaust pressure is atmospheric.What is the lowest possible exhaust temperature? How much work is obtained? You may assume ideal gas
What is the minimum amount of work required to separate an inlet stream of air fl owing at 20°C and 1 bar into exit streams of pure O2 and pure N2 at 20°C and 1 bar?
An adiabatic turbine is designed to take stream of steam fl owing at 10 kg/s from an inlet at 10 bar and 500°C to an outlet at 1 bar. It is reported that at steady-state, this turbine can deliver
An ideal gas at a fl ow rate of 10.0 m3/min enters a compressor at 25°C and 1 bar. It leaves at 1 MPa. During this process, heat is dissipated to the surroundings at a rate of 2100 W. You may take
Consider a Carnot (reversible) power cycle operating between a hot reservoir of 727°C and a cold reservoir of 27°C. If 700 W of power are generated, calculate the total entropy change of the
An ideal gas enters an adiabatic turbine with a molar fl ow rate of 10 [mol/s]. The inlet pressure is 100 bar, and the inlet temperature is 500°C. The gas exits at 1 bar. The ideal gas heat capacity

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