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engineering
introductory chemical engineering thermodynamics

Engineering And Chemical Thermodynamics 2nd Edition Milo D. Koretsky - Solutions

The process that you are designing requires that a vapor mixture of benzene and propane enter a holding tank at 480 K and 2 MPa, and a benzene mole fraction of 0.6. The design specifi es that 100 kg of vapor are in the tank. What volume must the tank be?(a) Calculate using the ideal gas
You are planning an experiment in which you have a mixture of 5 moles of hydrogen (H2).4 moles of water (H2O), and 1 of mole ethane (C2H6). You want to calculate the pressure of this mixture to determine which material to use to construct the vessel to contain these gases. The vessel needs to be
The following second virial coeffi cients have been reported for a mixture of n-butane (1) and carbon dioxide (2) at 313.2 K.From these data, do the following:(a) Predict the molar volume of a mixture of 25 mol % butane in carbon dioxide at 313.2 K and 10 bar.(b) Estimate the value of the binary
Re-solve Example 4.9 using the text software, ThermoSolver. Compare your answer to the answer that is given in the example.Example 4.9Calculate an expression for the second virial coeffi cient, B, for the hard sphere potential model.
Solve the following using ThermoSolver:(a) In Species Database, select Ethane. Report its critical temperature and pressure and Δhf,298 o .(b) In Saturation Pressure Calculator, fi nd the saturation temperature of ethane at 40 bar.(c) In Equation of State Solver, fi nd the volume and
As best as you can, compare the strength of the dipole–dipole, induction, and dispersion interactions for each of the following pure species at 298 K: H2O, NH3, CH4, CH3Cl, CCl4. Discuss the results.
Consider a mixture of Ar and HCl. Predict the relative importance of the van der Waals interactions of the different “two-body” interactions in the mixture. Compare the unlike interactions to that which is obtained from prediction using the geometric mean of the like interactions.
Consider the following molecules: CCl4, CF4, SiCl4. List these species in order of their total van der Waals forces of attraction, C6, from the largest value to the smallest. Explain your choice based on molecular arguments.
Determine the saturation pressure, Psat, of water and methanol at 100°C, 50°C, and 25°C.Report values in [Pa]. Based on intermolecular forces explain (i) why the vapor pressure of methanol at a given temperature is greater than water and (ii) why vapor pressure increases with temperature.
Consider the following molecules: CCl4, CF4, SiCl4, SiCl3H.(a) List these species in order of their van der Waals constant a, from the largest value of a to the smallest. Explain your choice based on molecular arguments.(b) Repeat for the van der Waals constant b. Explain your choice based on
At the critical point, the three roots in volume to a cubic equation must converge. Thus,Use Equation (E4.7A) to write the van der Waals parameters a and b in terms of the critical pressure and temperature. (v - vc) = 0 (E4.7A)
Show that a Taylor series expansion for the compressibility factor, z, about temperature, T, and concentration, c = 1/v, gives the form of the virial equation shown in Equation (4.26).
Calculate an expression for the second virial coeffi cient, B, for the hard sphere potential model.
Calculate the second virial coeffi cient, B, for CH4 over the temperature range 100–900 directly from the Lennard-Jones parameters. Compare the values to the following data reported in the literature. T[K] B [cm/mol] T[K] B [cm/mol] 110 -330 225 -83 120 130 -273 - 235 250 -66 275 -53 140 150 160
Determine the molar volume of copper at 500°C from the data in Table 4.4. TABLE 4.4 Molar Volume, Thermal Expansion Coefficient, and Isothermal Compressibility of Some Liquid and Solid Species at 20C and 1 bar v[cm/mol] B[K-] 10 K[Pa ] x 1010 Liquid Acetone Benzene Methanol Ethanol n-Hexane
Calculate the volume occupied by 10 kg of butane at 50 bar and 60°C using the Redlich–Kwong equation and the generalized compressibility charts.
Calculate the following:(a) The volume occupied by 20 kg of propane at 100°C and 70 bar(b) The pressure needed to fi ll a 0.1 m3 -vessel at room temperature to store 50 mol of propane(c) The pressure needed to fi ll a 0.1 m3-vessel at room temperature to store a mixture of 20 mol of propane and 30
Consider the following partial derivatives. For an ideal gas, state whether the value is positive, negative, zero, close to zero, or you cannot tell. Explain your answer. () () 1) //
Consider the following partial derivatives. For an ideal gas, state whether the value is positive, negative, zero, close to zero, or you cannot tell. Explain your answer. h aT P as P ah T T aT h
Consider the following partial derivatives. For a real gas dominated by attractive interactions, state whether the value is positive, negative, zero, close to zero, or you cannot tell. Explain your answer. u (2) (2) (*), (-), 1) 19 T T
Consider the following partial derivatives. For a real gas dominated by attractive interactions, state whether the value is positive, negative, zero, close to zero, or you cannot tell. Explain your answer. (x) () (), (~), (*), P P T T h
Develop an expression for the cyclic relation by equating z = z(x, y) and y = y(x, z).
One mole of propane gas is to be expanded from 0.001 m3 to 0.040 m3 while in contact with a heating bath that keeps the temperature constant at 100ºC. The expansion is not reversible. The heat extracted from the bath is 10.4 KJ. Using the van der Waals equation of state, determine the work for the
You have a glass of water and a glass of wine, as shown in the fi gure. You perform the following processes. (1) transfer 1 teaspoon of water to the glass of wine and mix thoroughly; then(2) transfer 1 teaspoon of this contaminated wine to the water. Now both the water and the wine are
You have a jar of 90 nickels and a jar of 90 pennies. You perform the following processes.(1) Transfer 10 nickels to the jar of pennies and mix thoroughly; then (2) transfer 10 coins from the contaminated pennies back to the jar with nickels. Which of the following is true? Explain.(a) The amount
Shown in the following fi gure is a process from which Species A is isothermally compressed from 0.5 bar and 300 K to 1 bar. The insets of each state, which are of equal volume, contain a“molecular view” of species A.Next consider the open system shown in the following fi gure. Species A fl ows
Go to the teaching or research labs at your university and determine three ways temperature is measured and three ways pressure is measured.
Consider a binary mixture of a light gas a with mass ma and a heavy gas b with mass mb at temperature T. How does the mean-square velocity of the two species compare? Which species, on average, moves faster?
Consider the system sketched below:(a) After a short time, is this system in equilibrium?(b) After a long time?(c) After a very long time? Large reservoir of boiling water (100 C) Cu Block Large reservoir of ice water (0 C)
Consider a tightly capped water bottle containing two phases with a small amount of liquid water and saturated air. If the bottle is left in the sun on a hot day and the temperature increases, what happens to the amount of water in the liquid? Explain.
A rigid, sealed container initially contains pure water at 100°C. Some of the water is in the liquid phase, and some is in the vapor phase (i.e., as steam). Air is then injected into the system in an isothermal process at constant volume. What happens?
Using language a high school student could understand, explain the difference between saturation pressure and vapor pressure.
This question addresses the two piston-cylinder assemblies depicted on the left of Figure 1.8 that illustrate the concept of saturation pressure. The piston on the right is at twice the pressure of the system on the left; however, if you count molecules of species a, there are less than twice the
Sometimes a lid to a pot used for cooking fi ts “too well” and can be diffi cult to remove after the pot cools down. Why do you think this is happening?
I thoroughly infl ated a bag of soccer balls last summer. However, when I brought them out to play this winter, they all were underinfl ated. Discuss the possible reasons.
Relative humidity is defi ned as the ratio of the mass of water in air divided by the mass of water at saturation. Compare the water content in the air on a day on which the temperature is 10°C with 90% relative humidity to a day at 30°C and 50% relative humidity. Which day has higher water
When a system contains regions that differ in physical structure or chemical composition, an overall value can be assigned to its properties. Consider the system, system 1, shown below. It contains na molecules in state a and nb molecules in state b.(a) Develop an expression for the extensive
Consider two systems of ideal gases. System I consists of pure gas A at a given pressure and temperature. System II contains a mixture of gases A and B at the same temperature and pressure.If the molecular weight of gas B is larger than gas A, how does the molar density (mol/cm3) of system I
Consider two systems of ideal gases. System I consists of pure gas A at a given pressure and temperature. System II contains a mixture of gases A and B at the same temperature and pressure.If the molecular weight of gas B is larger than gas A, how does the mass density 1g/cm3 2 of system I compare
You can breathe in approximately 2 L of air into your lungs. What volume of helium do you think you can breathe in? Explain.
A “pressure cooker” is a device that allows food to be cooked at pressures that are higher than atmospheric pressure. Explain why this device changes how your food is cooked.
The ideal gas model is one example of an equation of state. Why do you think it is termed an equation of state?
Consider a system containing water in the following states. What phases are present? (a) P = 10 [bar]; T = 170 [C] (b) = 3 [m/kg]; T = 70 [C] (c) P = 60 [bar]; 6 = 0.05 [m/kg] (d) P = 5 [bar]; s = 7.0592 [kJ/(kg K)]
Estimate the speed at which the average oxygen molecule is moving in the room that you are in.
The Reamur temperature scale uses the normal freezing and boiling points of water to defi ne 0°and 80°, respectively. What is the value of room temperature (22°C) on the Reamur scale?
At what temperature does water boil on the top of Mount Everest, elevation z = 8848 m?Recall that the dependence of pressure with altitude is given by:where, Patm is atmospheric pressure, g is the gravitational acceleration, and MW is the molecular weight of the gas. P = Patm exp MWgz RT
Water is cooled in a rigid closed container from the critical point to 10 bar. Determine the quality of the fi nal state.
Using linear interpolation, estimate the specifi c volume of water under the following conditions using data from the steam tables:Look up the specifi c volumes of water that correspond to cases (a), (b), and (c) on the website http://webbook.nist.gov/chemistry/fl uid/ and report their values.
Determine the mass of 1 L of saturated liquid water at 25°C. How do you think this value compares to the mass of 1L of subcooled liquid water at 25°C and atmospheric pressure?
Determine the temperature, quality, and internal energy of 5 kg of water in a rigid container of volume 1 m3 at a pressure of 2 bar.
A rigid container of volume 1 m3 contains saturated water at 1 MPa. If the quality is 0.10, what is the volume occupied by the vapor?
Use the data in the steam tables to plot the vapor–liquid dome on a Pv diagram. It is useful to plot v on a log scale. TABLE B.1 Saturated Water: Temperature Table T , C m/kg 0.01 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 P kPa, MPa 0.6113 kPa 0.8721 1.2276 1.7051 2.3385 3.1691
Calculate the volume of water using the ideal gas model under the following conditions.Then report the percent error when compared to the values reported in the steam tables. (a) P = 1.01 [bar]; T = 100 [C] (b) P = 1 [bar]; T = 500 [C] (c) P= 100 [bar]; T = 500 [C] (d) P = 100 [bar]; T = 1000 [C]
How many moles of air are in the room in which you are sitting? What is its mass?
Consider a gas at 20°C and 1 bar. The molecules may be considered to be hard spheres with a diameter of 3 Å. Estimate the percentage of the available volume they occupy.
You want to keep your house dry enough so that water does not condense on your walls at night. If the temperature gets down to 40°F at night, what is the maximum allowable density of water in the room during the day when the room is at 70°F?
Consider a rigid, thick-walled tube that is fi lled with H2O liquid and vapor at 0.1 MPa. After it is sealed, it is heated so that it passes through its critical point. What fraction of the mass in the tube is liquid?
As best as you can, estimate the specifi c volume of water at each of the following conditions.Justify your answer.(a) 2 bar and 200°C(b) 2 bar and 100°C
A rigid container contains 1 kg of water at 90°C. If 200 g of the water are in the liquid phase and the rest is vapor, determine the pressure in the tank and the volume of the tank.
40 g of water are sealed in a 10 L container at 300°C. As accurately as you can, determine the pressure of the container.
A rigid container of 100 L contains saturated water at 100°C. The water is heated, and it reaches the critical point. Determine the initial mass of water in the tank and its quality.
A piston-cylinder assembly contains 0.5 kg of water at 50°C and 500 kPa. It is then isobarically heated until all the water is vaporized. What is the fi nal temperature and volume?
In the two processes shown in the following fi gure, the same amount of heat, q, is supplied to equal amounts (in moles) of different gases, gas A and gas B. Both gases are initially at room temperature. The heat capacity of gas A is greater than the heat capacity of gas B. These processes take
In the two processes shown in the following fi gure, the same amount of heat, q, is supplied to the same gas, gas A. In both processes, the initial temperature and initial number of moles are equal. Process 1 occurs at constant volume; process 2 occurs at constant pressure.(a) Which gas has the
In the steady-state process shown in the following fi gure, steam fl ows through a porous plug, and its pressure drops from 10 MPa to 1 bar. Does the temperature increase, stay the same, or decrease? Explain. Water T P = 10 MPa Porous plug T P = 1 bar
In the steady-state process shown in the following fi gure, air fl ows through a turbine. Does the temperature increase, stay the same, or decrease? Explain. Air in P T Turbine Air out P T
In the steady-state process shown in the following fi gure, an ideal gas fl ows through a porous plug, and its pressure drops from 10 MPa to 1 bar. Does the temperature increase, stay the same, or decrease? Explain. Ideal Gas T P= 10 MPa Porous plug T P2 = 1 bar
An ideal gas fl ows into a well-insulated tank that is initially at vacuum, as shown in the following fi gure. How does T2 compare to Tin (higher, the same, or lower)? Explain.
State the conditions under which the following equations apply (try to be as specifi c as you can with the limitations).
Four processes are shown in the following fi gure. Each process occurs in a well-insulated piston cylinder assembly and starts from the same initial state, state 1. Put the fi nal temperatures in order from highest to lowest. Explain. In Process A, a large block of mass, M, is removed from the
In Example 2.4, we solved a problem where 10.0 kg of water was reversibly compressed in a piston–cylinder assembly from a pressure of 20 bar and a volume of 1.0 m3 to a pressure of 100 bar.In this example, the work was calculated to bethe heat wasand the final temperature was T2 =
Consider a cup of cold water. Come up with and sketch as many ways as you can think of to raise the temperature of the water.
Consider the compression of a spring by placing a large mass on it. The degree to which the spring compresses is related to its spring constant, k. The force exerted by the spring on the mass is given by:where x represents the distance the spring compresses from its relaxed position. Does the
If you sprinkle water on a very hot skillet, it will evaporate. However, you get the paradoxical result that at higher temperatures the water drops take longer to evaporate than at lower temperatures. Explain this result.
On a hot summer day, your roommate suggests that you open the refrigerator to cool off your apartment. Choosing the entire apartment as the system, perform a fi rst-law analysis to decide whether this idea has merit.
Take a thick rubber band and expand it by stretching it. If you hold it to your lips, you will sense that it is hotter. However, we have seen that the temperature of a gas in a piston–cylinder assembly cools upon expansion. Explain these opposite results in the context of an energy balance.
Explain why ice often forms on the valve of a tank of compressed gas (high pressure) when it is opened to the atmosphere and the gas escapes. Where does the H2O come from?
You are making plans to stay warm in the winter. Due to your busy schedule, you are typically away from your house all day. You know it costs a lot to operate the electric heaters to keep your house warm. However, you have been told that it is more effi cient to leave your house warm all day rather
The normal human body temperature is approximately 37°C. For normal metabolic processes, it is important to maintain the body at this temperature. Hypothermia is a condition when the core body temperature drops below 35°C. You may assume the body contains 60% water.
(a) What requires more heat input: to raise the temperature of a gas in a constant-pressure cylinder or in a constant-volume bomb? Explain.(b) Explain why you feel less comfortable on a hot summer day when the (relative) humidity is higher even though the temperature is the same.
Consider that towel you used to dry yourself with after your last shower. After being washed it must be dried so it can be used again. Estimate how much energy it takes to dry the towel after it has been washed. State all assumptions that you make. Now consider the dryer in your dwelling (or at the
A rigid container contains saturated water at a pressure of 2 bar and a quality of 0.42. The water undergoes a process in which it is heated to a fi nal temperature of 540°C. Determine the fi nal pressure of the container, and the energy transferred by work and by heat during this process.
Consider the piston–cylinder assembly containing 0.20 kg of pure water, as shown in the following fi gure. The cross-sectional area of the piston is 0.50 m2, and its initial height is 0.7172 m above the base of the cylinder. The initial pressure is 1.0 bar. A spring with a linear spring
Consider boiling water to make a pot of tea. Say it takes roughly 10 min to bring 1 L of H2O taken from the tap at 25ºC to boil. What is the total heat input, Q? What is the rate of heat input, Q?
Consider a process that takes steam from an initial state where P = 1 bar and T = 400°C to a state where P = 0.5 bar and T = 200°C. Calculate the change in internal energy for this process using the following sources for data:(a) the steam tables;(b) ideal gas heat capacity.
Consider a piston–cylinder assembly that contains 2.5 L of an ideal gas at 30ºC and 8 bar.The gas reversibly expands to 5 bar.(a) Write an energy balance for this process (you may neglect changes in potential and kinetic energy).(b) Suppose that the process is done isothermally. What is the
Five moles of nitrogen are expanded from an initial state of 3 bar and 88ºC to a fi nal state of 1 bar and 88ºC. You may consider N2 to behave as an ideal gas. Answer the following questions for each of the following reversible processes:(a) The fi rst process is isothermal expansion.(i) Draw
A 5-kg aluminum block sits in your lab, which is at 21ºC. You wish to increase the temperature of the block to 50ºC. How much heat in [J] must be supplied?
A piston–cylinder assembly contains 3 kg of steam at a pressure of 100 bar and a temperature of 400ºC. It undergoes a process whereby it expands against a constant pressure of 20 bar, until the forces balance. During the process, the piston generates 748,740 [J] of work. Water is not an ideal
Consider a piston–cylinder assembly that contains 1 mole of ideal gas, A. The system is well insulated. Its initial volume is 10 L and initial pressure, 2 bar. The gas is allowed to expand against a constant external pressure of 1 bar until it reaches mechanical equilibrium. Is this a reversible
For the well-insulated piston–cylinder assembly containing 1 mole of ideal gas described in Problem 2.28, describe the process by which you can obtain the maximum work from the system.Calculate the value for the work. What is the fi nal temperature? Why is T lower than that calculated in Problem
The insulated vessel shown below has two compartments separated by a membrane. On one side is 1 kg of steam at 400ºC and 200 bar. The other side is evacuated. The membrane ruptures, fi lling the entire volume. The fi nal pressure is 100 bar. Determine the fi nal temperature of the steam and the
A membrane divides a rigid, well-insulated 2 - m3 tank into two equal parts. The left side contains an ideal gas [cP = 30 J/ 1mol K2 ] at 10 bar and 300 K. The right side contains nothing; it is a vacuum. A small hole forms in the membrane, gas slowly leaks out from the left side, and eventually
A well-insulated rigid container contains two 10 L compartments initially at 300 K. Each compartment contains argon gas. The compartments are separated by a well-insulated piston that is held in place by a restraining pin. One compartment is initially at a pressure of 1 bar and the other is at 5
You have 0.4 mol of gas A within a piston–cylinder assembly. The initial pressure is 20 bar, and the initial temperature is 675 K. The system then undergoes an adiabatic process where the piston expands against constant external pressure of 1 bar until the forces balance.(a) What is the fi nal
One kg of liquid n-octane (C8H18) is placed in a closed rigid container with 50% excess air at 100°C and 1 bar. It undergoes an isothermal process in which it reacts and completely combusts to form CO2 (g) and H2O (g). State any assumptions that you make in solving this problem. Take the heat
Repeat Problem 2.34, except consider now the combustion products contain CO (g) as well as CO2 (g) and H2O (g) with the ratio of CO2/CO produced being 4/1. All other conditions remain the same as in Problem 2.34.Problem 2.34One kg of liquid n-octane (C8H18) is placed in a closed rigid container
Approximately half the dry mass of the human body consists of proteins. The backbone of a protein is a long polypeptide chain. In its natural or “native” state, the protein folds back on itself and is held together by a large number of intramolecular interactions, which include van der Waals
Fuel cells are a promising alternative energy technology. They are based on producing energy by the following reaction:One type of fuel cell, the solid oxide fuel cell, operates at high temperatures. A solid oxide fuel cell is fed 0.32 mol/s H2 and 0.16 mol/s O2, and the reaction goes to
Consider a piston–cylinder assembly containing 10 kg of water. Initially the gas has a pressure of 20 bar and occupies a volume of 1.0 m3. Under these conditions, water does not behave as an ideal gas.(a) The system now undergoes a reversible process in which it is compressed to 100 bar. The

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