Questions and Answers of Introductory Chemical Engineering Thermodynamics

A rigid tank of volume 0.1 m3 is fi lled from a supply line at 127°C and 2 bar, as drawn in the following fi gure. It is initially at vacuum. The valve is opened, and the tank fi lls until the
A rigid tank of volume 0.5 m3 is connected to a piston–cylinder assembly by a valve as shown below. Both vessels contain pure water. They are immersed in a constant-temperature bath at 200°C and
A rigid, well-insulated container is initially divided into three compartments. The top compartment contains a vacuum. It is separated from the middle compartment A by a frictionless mass of 1000 kg
Consider the system shown below. Tank A has a volume of 0.3 m3 and initially contains an ideal diatomic gas at 700 kPa, 40°C. Cylinder B has a piston resting on the bottom, at which point the spring
A steam turbine in a small electric power plant is designed to accept 4500 kg/hr of steam at 60 bar and 500°C and exhaust the steam at 10 bar. Heat transfers to the surroundings 1Tsurr 5 300K2 at a
Air fl owing at 1 m3/s enters an adiabatic compressor at 20°C and 1 bar. It exits at 200°C. The isentropic effi ciency of the compressor is 80%. Calculate the exit pressure and the power required.
Steam enters a turbine at 10 MPa and 500°C and leaves at 100 kPa. The isentropic effi ciency of the turbine is 85%. Calculate the exit temperature and the work generated per kg of steam fl owing
Nitrogen gas at 27°C fl ows into a well-insulated device operating at steady-state. There is no shaft work. The device has two exit streams. Two-thirds of the nitrogen, by mass, exits at 127°C and
Consider a well-insulated piston–cylinder assembly containing 5 kg of water vapor, initially at 540°C and 60 bar, that undergoes a reversible expansion to 20 bar. The surroundings are at 1 bar and
Consider a well-insulated, rigid tank containing 5 kg of water vapor in the same initial state as in Problem 3.52 (540°C, 60 bar). Again, the surroundings are at 1 bar and 25°C, as shown below.A
Consider fi lling a “type A” gas cylinder with water from a high-pressure supply line as shown on next page. Before fi lling, the cylinder is empty (vacuum). The valve is then opened, exposing
A rigid tank has a volume of 0.01 m3. It initially contains saturated water at a temperature of 200°C and a quality of 0.4. The top of the tank contains a pressure-regulating valve that maintains
Consider the system sketched below in which a turbine is placed between two rigid tanks. Tank 1 initially contains an ideal gas at 10 bar and 1000 K. Its volume is 1 m3. Tank 2 is 9 m3 and is
A hot reservoir is available at 500°C and a cold reservoir at 25°C. Calculate the maximum possible effi ciency of a power cycle that operates between these two reservoirs.
An ideal Rankine cycle operates with the following design: 100 kg/s of steam enters the turbine at 30 bar and 500°C and is condensed at 0.1 bar. Determine the power produced and the effi ciency of
Come up with four ways in which you can make the power cycle of Problem 3.58 more efficient. Illustrate how your ideas achieve increased effi ciency using sketches like that in Figure 3.8.Problem
An ideal Rankine cycle produces 100 MW of power. If steam enters the turbine at 100 bar and 500°C and is condensed at 1 bar, determine the mass fl ow rate of steam. Recalculate the mass fl ow rate
Consider a refrigeration system based on an ideal vapor-compression cycle using R-134a as the refrigerant. It operates between 0.7 MPa and 0.12 MPa with a fl ow rate of 0.5 mol/s. Calculate the
If the throttling valve in Problem 3.62 is replaced by an isentropic turbine, what is the COP? Is this modifi cation practical? Explain.Problem 3.62Consider a refrigeration system based on an ideal
A two-stage cascade refrigeration system is shown below. The refrigerant is R134a. It consists of two ideal vapor-compression cycles with heat exchange between the condenser of the lowertemperature
Design a vapor-compression refrigeration system to cool a system to 25°C with the capability for up to 20 kW of cooling. You have a reservoir at 20°C to reject heat to. Refrigerants and their
Modify the vapor-compression refrigeration system presented in Section 3.9 to apply to a refrigerator for home use. This system needs to provide cooling to two units: the freezer at 215°C and the
Consider an ideal, reversible magnetic refrigeration cycle shown in the fi gure on next page.A paramagnetic working material in the form of the rim of a wheel is rotated between a hightemperature
Consider the oxidation of cuprous oxide to form cupric oxide by the following reaction:Calculate Δsrxn. This task can be done in the same type of path described in Section 2.6 for Δhrxn.You can
Determine the exergy of the following states. Take the environment to be at 25°C and 1 bar.(a) Argon at 500 K and 2 bar(b) Propane at 500 K and 2 bar(c) Water at 500 K and 2 bar
Determine the exergy of a system of pure water containing 1 kg ice and 10 g water vapor at 220°C. Take the environment to be at 10°C and 1 bar.
1 kg of copper at 600°C and 1 bar is immersed in 20 kg of water at 20°C and 1 bar in a well-insulated container. Consider the system to be both the copper and the water. Calculate the change in
An ideal gas is contained in a piston–cylinder assembly. The pressure of the gas is initially balanced by two 2000 kg blocks plus the atmospheric pressure of 1 [bar]. The piston has a
Steam enters a turbine with a mass fl ow rate of 5 [kg/s]. The inlet pressure is 60 bar, and the inlet temperature is 500°C. The outlet contains saturated steam at 1 bar. The surroundings are at
1 mol of steam is initially at 10 bar and 200°C. The surroundings are at 20°C and 1 bar.(a) Calculate the exergy of the system.(b) Calculate the change in exergy for a process where the steam is
Ethylene (C2H4) at 100°C and 1 bar passes through a heater and emerges at 200°C. Calculate the change in exthalpy per mole of ethylene that passes through. You may assume ideal gas behavior. The
Consider a tank containing 100 kg of water initially at 70°C. Due to heat transfer, the temperature of water in the tank drops to 50°C. The surroundings are at 10°C. Calculate the lost work.
An open feedwater heater is used to take inlet stream of water vapor at 5 bar and 200°C and have it leave as saturated liquid at 5 bar. This is accomplished by mixing it with an appropriate amount
You wish to heat a stream of CO2 at pressure 1 bar, fl owing at 10 mol/s, from 150°C to 300°C in a countercurrent heat exchanger. To do this task, you are using a stream of high-pressure steam
An ideal gas at 6 MPa and 200°C is fl owing in a pipe, as shown in the following fi gure. Connected to this pipe through a valve is a tank of volume 0.4 m3. This tank initially is at vacuum. The
Steam at 6 MPa and 400°C is fl owing in a pipe. Connected to this pipe through a valve is a tank of volume 0.4 m3. This tank initially is at vacuum. The valve is opened, and the tank fi lls with the
In Section 2.3, we learned about reversible and irreversible processes in the context of a piston–cylinder assembly undergoing isothermal expansion and compression processes. Four of these
An insulated tank (V = 1.6628 L) is divided into two equal parts by a thin partition. On the left is an ideal gas at 100 kPa and 500 K; on the right is a vacuum. The partition ruptures with a loud
Consider an isolated system containing two blocks of copper with equal mass. One block is initially at 0ºC while the other is at 100ºC. They are brought into contact with each other and allowed to
Calculate the change in entropy when 1 mole of saturated ethanol vapor condenses at its normal boiling point.
Steam enters a nozzle at 300 kPa and 700ºC with a velocity of 20 m/s. The nozzle exit pressure is 200 kPa. Assuming this process is reversible and adiabatic determine(a) the exit temperature
In Example 2.21, we analyzed an open feedwater heater. Superheated water vapor at a pressure of 200 bar, a temperature of 500ºC, and a fl ow rate of 10 kg/s was brought to a saturated vapor state at
A piston–cylinder device initially contains 0.50 m3 of an ideal gas at 150 kPa and 20ºC. The gas is subjected to a constant external pressure of 400 kPa and compressed in an isothermal process.
Calculate the entropy change when 1 mole of air is heated and expanded from 25ºC and 1 bar to 100ºC and 0.5 bar.
One mole of pure N2 and 1 mole of pure O2 are contained in separate compartments of a rigid container at 1 bar and 298 K. The gases are then allowed to mix. Calculate the entropy change of the mixing
In Section 2.7, we came up with the following expression for a reversible, adiabatic process on an ideal gas with constant heat capacity, based on fi rst-law analysis:Come up with the same equation
Consider a cylinder containing 4 moles of compressed argon at 10 bar and 298 K. The cylinder is housed in a big lab maintained at 1 bar and 298 K. The valve develops a leak and Ar escapes to the
An ideal gas enters a turbine with a fl ow rate of 250 mol/s at a pressure of 125 bar and a specifi c volume of 500 cm3/mol. The gas exits at 8 bar. The process operates at steady-state. Assume the
In an actual expansion through the turbine of Example 3.12, 22.1 [MW] of power is obtained. What is the isentropic effi ciency, hturbine, for the process? The isentropic effi ciency is given by:
Steam enters the turbine in a power plant at 600ºC and 10 MPa and is condensed at a pressure of 100 kPa. Assume the plant can be treated as an ideal Rankine cycle. Determine the power produced per
Redo the analysis of the Rankine cycle of Example 3.14 but include isentropic effi ciencies of 85% in the pump and turbine. Determine the net power and the overall effi ciency of the power cycle.
It is desired to produce 10 kW of refrigeration from a vapor-compression refrigeration cycle. The working fl uid is refrigerant 134a. The cycle operates between 120 kPa and 900 kPa. Assuming an ideal
Consider a piston-cylinder assembly containing an ideal gas, initially at 20.0 bar and 1000 K. The initial volume is 1.6 L. The system undergoes a reversible process in which it is expands to 1 bar.
A shell and tube heat exchanger is designed to warm air from the environment by condensing steam that is passed through the tubes on the other side. The maximum air fl ow is 30 kg/min, and the air is
Magnetic refrigeration cycles can be used to achieve supercold temperatures. They typically operate between a “hot” reservoir at liquid helium temperature (4.4 K) and a cold reservoir at very low
Consider BClH2. In each of the following cases, when do you expect the compressibility factor to be closer to one. Explain.(a) At 300 K, 10 bar or at 300 K, 20 bar(b) At 300 K, 20 bar or 1000 K, 20
The Lennard-Jones potential function is often used to describe the molecular potential energy between two species. Rank each of the following sets of species, from largest to smallest, in terms of
Using your knowledge of intermolecular forces, explain the following observation:(a) At 300°C and 30 bar, the internal energy of water is less than at 300°C and 20 bar.(b) At 300 K and 30 bar,
Consider comparing 1 mole of NH3 at 10 bar and 500 K behaving as a real gas (i.e., considering its intermolecular interactions) vs. 1 mole of NH3 at 10 bar and 500 K behaving as an ideal gas (i.e.,
Consider comparing 1 mole of NH3 at 10 bar and 500 K vs. 1 mole of Ne at 10 bar and 500 K.Answer the following questions using molecular arguments. Explain your choice with diagrams and descriptions
The normal boiling points of some halide silanes are reported below. Explain the order in terms of intermolecular forces. Species Boiling point [C] SiCIF 3 - 70.0 SiBrF3 - 41.7 SiCl3F 12.2 SiBr3 F
Three isomers of C3H6O2 have the following normal boiling points: propanoic acid (CH3CH2COOH), 141°C; methyl acetate (CH3COOCH3), 58°C; and ethyl formate (HCOOCH2CH3), 53°C. Using your
Normal boiling points are shown for sets of species in the following tables. Explain the order based on your understanding of intermolecular interactions:(a) Alkyl halides(b) Alkanes Species Boiling
If the diatomic gas of Problem 3.47 were nonideal at the pressures in the problem and attractive forces dominate, qualitatively describe how the fi nal temperature in tank A would change from the
Consider a high-pressure tank at room temperature. It undergoes a process where a valve is opened and the gas escapes until the pressure reaches 1 bar.(a) The process is undertaken with an ideal
The second virial coeffi cient for argon is reported versus temperature in the following table.Explain the trend with temperature in terms of dominant intermolecular interactions. What can you say
Table 4.3 compares the van der Waals (1873), Redlich–Kwong (1949), and Peng–Robinson (1976) equations of state in similar forms. Based on intermolecular interactions, qualitatively analyze how
At very high temperatures, a gas can be ionized and remain in thermodynamic equilibrium.Consider the case of gas containing only ions, A1. Your supervisor requests that you come up with a simple
Consider a mixture of O2 (a) and C3H8 (b): (a) Write expressions for the attractive interactions Taa, Ibb, and Iab as a function of distance between the molecules, r. (b) How does I'ab compare to VTT
While returning to your dorm late last night with a hot cup of coffee, the heat overcomes you and, much to your chagrin, you drop the paper cup, spilling its entire contents. As you had just spent
The London force is directly related to the polarizabilities of the corresponding molecules.Consider the following table of molecular polarizability, a:From these data, come up with a model to
Consider 2 neighboring Ar atoms in a system of pure Ar at 25 bar and 300 K:(a) What is the average distance between them (in Å)?(b) Calculate the potential energy due to gravity (between the two
As discussed in the text, the repulsive term in the Lennard-Jones potential should have an exponential dependence rather than r-12. Graphically compare the features of the Lennard-Jones potential to
Calculate the bond strength in [eV] of a sodium ion in a crystal of NaCl. For the salt lattice: (a) Consider only the six nearest-neighbor Cl- ions. The Cl- ions are at a distance r = 2.76 . from the
Using data from Table 4.2, estimate the equilibrium bond length that would exist in a molecule of Xe2. TABLE 4.2 Lennard-Jones Parameters for Several Species /k(K) 10.2 35.7 Gas He H CH4 C6H6 288 28
Calculate the van der Waals parameter b for CH4, C6H6, and CH3OH. Based on these values, estimate the molecular diameter of each species. Compare the values obtained with those in Table 4.2. TABLE
Calculate the van der Waals parameter a for CH4, C6H6, and CH3OH. Based on these values, estimate the value of C6 for each species. Compare the values obtained with that calculated by Equation (4.8).
Consider a cylinder fi tted with a piston that contains 2 mol of H2O in a container at 1000 K.Calculate how much work is required to isothermally and reversibly compress this gas from 10 L to 1 L, in
Determine the second and third virial coeffi cients using the van der Waals equation of state.Begin by writing the van der Waals equation in compressibility factor form and performing a power-series
Determine the second and third virial coeffi cients using Redlich–Kwong equation of state. 1 1- x = 1 + x +x + 3 +
The Dieterici equation of state is given by:(a) Find an expression for the parameters a and b in terms of the critical properties Tc and Pc.(b) Find the compressibility factor at the critical
Verify Equations (4.28) by rewriting the expansion of the virial equation in pressure [Equation (4.27)] in terms of the virial expansion in the reciprocal of molar volume [Equation (4.26)]. Pu RT 1 +
Consider the Berthelot equation of state given below. Show how to calculate the constants a and b using only critical point data. P = RT v-b a Tv
Find the reduced form of the Berthelot equation of state. See Problem 4.29.Problem 4.29Consider the Berthelot equation of state given below. Show how to calculate the constants a and b using only
Calculate the saturation pressure of n-pentane at 90°C by applying the “equal area” rule to(a) the Redlich–Kwong equation;(b) the Peng–Robinson equation. Compare these results to the
At -30°C, the saturation pressure of ethane is 10.6 bar. Calculate the densities of the liquid and vapor phases using the Peng–Robinson equation. Compare to the reported values for the liquid and
Welcome to Beaver Gas Co.! Your fi rst task is to calculate the annual gross sales of our superpure-grade nitrogen and oxygen gases.(a) The total gross sales of N2 is 30,000 units. Take the volume
For the Redlich–Kwong equation, develop expressions for the parameters a and b, the equation reduced form, and the value of the compressibility factor at the critical point as a function of the
The square-well potential function is given by:Answer the following questions:(a) Sketch a plot of square-well potential energy versus distance.(b) Using this potential function, develop an
In this problem we seek to develop an expression for the van der Waals constants a and b in terms of molecular parameters using the Sutherland model for potential energy.(a) Show that writing the
Determine expressions for the thermal expansion coeffi cient, β, and the isothermal compressibility, k, for an ideal gas.
Using the steam tables, estimate the values for the thermal expansion coeffi cient, β,and the isothermal compressibility, k, of liquid water at 20°C and 100°C. Symbols Used in the Steam Tables T P
Use the Rackett equation to calculate the liquid-phase molar volume of each of the following species at the same temperature as the measured values reported. Which species had the greatest absolute
Calculate the following:(a) the volume occupied by 20 kg of ethane at 70°C and 30 bar(b) the pressure needed to fi ll a 0.1 m3-vessel at room temperature to store 40 kg of ethane
Calculate the volume occupied by 50 kg of propane at 35 bar and 50°C, using the following:(a) the ideal gas model(b) The Redlich–Kwong equation of state(c) The Peng–Robinson equation of state(d)
For a lecture-demonstration experiment, it is desired to construct a sealed glass vial containing a pure substance that can be made to pass through the critical point by heating the vial in a
Compare the compressibility factor of methane at Tr = 1.1 and Pr = 1.2 using the Peng–Robinson equation of state and the compressibility charts. Repeat the calculations for methanol.
Using the generalized compressibility charts, calculate the molar volume of ammonia at 92°C and 306.5 bar. What phase is ammonia in? GENERALIZED COMPRESSIBILITY CHARTS The principle of corresponding
Use the Redlich–Kwong equation to calculate the size of vessel you would need to contain 30 kg of acetylene mixed with 50 kg of n-butane at 30 bar and 450 K. The binary interaction coeffi cient is
You wish to use the Redlich–Kwong equation of state to describe a mixture of carbon dioxide (1) and toluene (2). To be as accurate as possible with the mixing rules, you want to include the binary

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