Questions and Answers of Introduction To Chemical Engineering Thermodynamics

Turbines can be used to recover energy from high-pressure liquid streams. However, they are not used when the high-pressure stream is a saturated liquid. Why? Illustrate by determining the downstream
A small adiabatic air compressor is used to pump air into a 20-m3 insulated tank. The tank initially contains air at 25°C and 101.33 kPa, exactly the conditions at which air enters the compressor.
Show that the points on the Joule/Thomson inversion curve [for which μ = (∂T/∂P)H = 0] are also characterized by each of the following: ze = 0; G), (*), (a) (b) = 0; (c) (d) = 0; T P dP. (e)
Demonstrate that the power requirement for compressing a gas is smaller the more complex the gas. Assume fixed values of ṅ, η, T1, P1, and P2, and that the gas is ideal with constant heat
Air is compressed in a steady-flow compressor, entering at 1.2 bar and 300 K and leaving at 5 bar and 500 K. Operation is nonadiabatic, with heat transfer to the surroundings at 295 K. For the same
A boiler house produces a large excess of low-pressure [50(psig), 5(°F)-superheat] steam. An upgrade is proposed that would first run the low-pressure steam through an adiabatic steady-flow
Liquid benzene at 25°C and 1.2 bar is converted to vapor at 200°C and 5 bar in a twostep steady-flow process: compression by a pump to 5 bar, followed by vaporization in a counterflow heat
Operating data are taken on an air turbine. For a particular run, P1 = 8 bar, T1 = 600 K, and P2 = 1.2 bar. However, the recorded outlet temperature is only partially legible; it could be T2 = 318,
The infinite heat reservoir is an abstraction, often approximated in engineering applications by large bodies of air or water. Apply the closed-system form of the energy balance [Eq. (2.3)] to such a
Liquid benzene at 25°C and 1.2 bar is converted to vapor at 200°C and 5 bar in a two-step steady-flow process: vaporization in a counter flow heat exchanger at 1.2 bar, followed by
Of the processes proposed in Probs. 7.50 and 7.51, which would you recommend? Why?Problem 7.50Liquid benzene at 25°C and 1.2 bar is converted to vapor at 200°C and 5 bar in a twostep steady-flow
Liquids (identified below) at 25°C are completely vaporized at 1(atm) in a countercurrent heat exchanger. Saturated steam is the heating medium, available at four pressures: 4.5, 9, 17, and 33 bar.
Show how the general rate form of the entropy balance, Eq. (5.16), reduces to Eq. (5.2) for the case of a closed system.Eq. (5.16)Eq. (5.2) d(mS)cv + A(Sm)fs- E = ŠG 2 0 To.j (5.16) dt
Consider the direct heat transfer from a heat reservoir at T1 to another heat reservoir at temperature T2, where T1 > T2 > Tσ. It is not obvious why the lost work of this process should depend
Four different types of drivers for gas compressors are: electric motors, gas expanders, steam turbines, and internal-combustion engines. Suggest when each might be appropriate. How would you
Consider the air conditioning of a house through use of solar energy. At a particular location, experiment has shown that solar radiation allows a large tank of pressurized water to be maintained at
Two schemes are proposed for the reduction in pressure of ethylene gas at 375 K and 18 bar to 1.2 bar in a steady-flow process:(a) Pass it through a throttle valve.(b) Send it through an adiabatic
An ideal gas at 2500 kPa is throttled adiabatically to 150 kPa at the rate of 20 mol·s–1. Determine ṠG and Ẇlost if Tσ = 300 K.
Consider the heating of a house by a furnace, which serves as a heat source reservoir at a high temperature TF. The house acts as a heat sink reservoir at temperature T, and heat |Q| must be added to
Prove that the mean heat capacities ⟨CP⟩H and ⟨CP⟩S are inherently positive, whether T > T0 or T < T0. Explain why they are well defined for T = T0.
Reversible adiabatic processes are isentropic. Are isentropic processes necessarily reversible and adiabatic? If so, explain why; if not, give an illustrative example.
A mass m of liquid water at temperature T1 is mixed adiabatically and isobarically with an equal mass of liquid water at temperature T2. Assuming constant CP, showand prove that this is positive.
For an ideal gas prove that: AS c dT V + In, Vo R To R T
A heat engine operating in outer space may be assumed equivalent to a Carnot engine operating between reservoirs at temperatures TH and TC . The only way heat can be discarded from the engine is by
A Carnot engine operates between two finite heat reservoirs of total heat capacity C tH and CtC(a) Develop an expression relating TC to TH at any time.(b) Determine an expression for the
For an ideal gas with constant heat capacities, show that:(a) For a temperature change from T1 to T2, ΔS of the gas is greater when the change occurs at constant pressure than when it occurs at
An ideal gas, CP = (7/2)R, is heated in a steady-flow heat exchanger from 70°C to 190°C by another stream of the same ideal gas which enters at 320°C. The flow rates of the two streams are the
With respect to 1 kg of liquid water:(a) Initially at 0°C, it is heated to 100°C by contact with a heat reservoir at 100°C. What is the entropy change of the water? Of the heat reservoir? What is
Which is the more effective way to increase the thermal efficiency of a Carnot engine: to increase TH with TC constant, or to decrease TC with TH constant? For a real engine, which would be the
A natural-gas fuel contains 85 mol-% methane, 10 mol-% ethane, and 5 mol-% nitrogen.(a) What is the standard heat of combustion (kJ·mol−1) of the fuel at 25°C with H2O(g) as a product?(b) The
Saturated water vapor, i.e., steam, is commonly used as a heat source in heat-exchanger applications. Why saturated vapor? Why saturated water vapor? In a plant of any reasonable size, several
The first step in the metabolism of ethanol is dehydrogenation by reaction with nicotinamide-adenine dinucleotide (NAD):
Compute the standard heat of reaction for each of the following reactions taking place at 298.15 K in dilute aqueous solution at zero ionic strength.(a) D-Glucose + ATP2− → D-Glucose
Determine the standard heat for one of the reactions of Prob. 4.23: part (a) at 600°C, part (b) at 50°C, part (f) at 650°C, part (i) at 700°C, part (j) at 590(°F), part (l) at 770(°F), part (m)
Determine the standard heat of each of the following reactions at 25°C:(a) N2(g) + 3H2(g) → 2NH3(g)(b) 4NH3(g) + 5O2(g) → 4NO(g) + 6H2O(g)(c) 3NO2(g) + H2O(l) → 2HNO3(l) + NO(g)(d) CaC2(s) +
What is the standard heat of combustion of each of the following gases at 25°C if the combustion products are H2O(l) and CO2(g)? Compute both the molar and specific heat of combustion in each
For each of the following substances, compute the final temperature when heat in the amount of 60 kJ·mol−1 is added to the subcooled liquid at 25°C at atmospheric pressure.(a) Methanol(b)
A process stream is heated as a gas from 25°C to 250°C at constant P. A quick estimate of the energy requirement is obtained from Eq. (4.3), with CP taken as constant and equal to its value at
If the heat capacity of a substance is correctly represented by an equation of the form, CP  = A + BT + DT−2 show that the error resulting when ⟨CP⟩H is assumed equal to CP
If the heat capacity of a substance is correctly represented by an equation of the form, CP  = A + BT + CT2 show that the error resulting when ⟨CP⟩H is assumed equal to CP
For a steady-flow heat exchanger with a feed temperature of 100°C, compute the outlet stream temperature when heat in the amount of 12 kJ·mol−1 is added to the following substances.(a) Methane(b)
Given below are four proposed modifications of the van der Waals equation of state. Are any of these modifications reasonable? Explain carefully; statements such as, “It isn’t cubic in volume”
With reference to Prob. 2.47, assume air to be an ideal gas, and develop an expression giving the household air temperature as a function of time.Problem 2.47The heating of a home to increase its
A garden hose with the water valve shut and the nozzle closed sits in the sun, full of liquid water. Initially, the water is at 10°C and 6 bar. After some time the temperature of the water rises to
Derive the values of Ω, Ψ, and Zc given in Table 3.1 for:(a) The Redlich/Kwong equation of state.(b) The Soave/Redlich/Kwong equation of state.(c) The Peng/Robinson equation of state.Table 3.1
Suppose Z vs. Pr data are available at constant Tr . Show that the reduced density-series second virial coefficient can be derived from such data via the expression: B = lim (Z – 1)ZT,/P, В %D P,-0
Write the general form of an equation of state as: Z = 1 + Zrep (ρ) − Zattr
Show that the density-series second virial coefficients can be derived from isothermal volumetric data via the expression: B = lim(Z – 1)/p p-0 p(molar density)= 1/V -
Figure 3.3 suggests that the isochores (paths of constant volume) are approximately straight lines on a P-T diagram. Show that the following models imply linear isochores.(a) Constant-β, κ equation
For a gas described by the Redlich/Kwong equation and for a temperature greater than Tc, develop expressions for the two limiting slopes,Note that in the limit as P → 0, V → ∞, and that in the
Recreational scuba diving using air is limited to depths of 40 m. Technical divers use different gas mixes at different depths, allowing them to go much deeper. Assuming a lung volume of 6 liters,
For one of the substances in Prob. 3.62, estimate the mass of the substance contained in the size D cylinder at 20°C and 25 bar.Problems 3.62A size D compressed gas cylinder has an internal volume
A size D compressed gas cylinder has an internal volume of 2.40 liters. Estimate the pressure in a size D cylinder if it contains 454g of one of the following semiconductor process gases at 20°C:(a)
Estimate:(a) The mass of ethane contained in a 0.15 m3 vessel at 60°C and 14,000 kPa.(b) The temperature at which 40 kg of ethane stored in a 0.15 m3 vessel exerts a pressure 20,000 kPa.
One mole of an ideal gas with constant heat capacities undergoes an arbitrary mechanically reversible process. Show that: AU=- 7-14(PV)
A substance for which κ is a constant undergoes an isothermal, mechanically reversible process from initial state (P1, V1) to final state (P2, V2), where V is molar volume.(a) Starting with the
For one of the substances in Table 3.2, compute the final pressure when the substance is heated from 15°C and 1 bar to 25°C at constant volume.Table 3.2 Table 3.2: Volumetric Properties of Liquids
How many phase rule variables must be specified to fix the thermodynamic state of each of the following systems?(a) A sealed flask containing a liquid ethanol-water mixture in equilibrium with its
A renowned laboratory reports quadruple-point coordinates of 10.2 Mbar and 24.1°C for four-phase equilibrium of allotropic solid forms of the exotic chemical β-miasmone. Evaluate the claim.
A closed, nonreactive system contains species 1 and 2 in vapor/liquid equilibrium. Species 2 is a very light gas, essentially insoluble in the liquid phase. The vapor phase contains both species 1
For the system described in Prob. 3.4:(a) How many phase-rule variables in addition to T and P must be chosen so as to fix the compositions of both phases?(b) If the temperature and pressure are to
The Tait equation for liquids is written for an isotherm as:where V is molar or specific volume, V0 is the hypothetical molar or specific volume at zero pressure, and A and B are positive constants.
Various species of hagfish, or slime eels, live on the ocean floor, where they burrow inside other fish, eating them from the inside out and secreting copious amounts of slime. Their skins are widely
For one of the substances in Table 3.2, compute the change in volume and work done when one kilogram of the substance is heated from 15°C to 25°C at a constant pressure of 1 bar.Table 3.2 Table
For one of the substances in Table 3.2, compute the change in volume and work done when one kilogram of the substance is compressed from 1 bar to 100 bar at a constant temperature of 20°C.Table 3.2
One mole of an ideal gas with CP = (7/2)R and CV = (5/2)R expands from P1 = 8 bar and T1 = 600 K to P2 = 1 bar by each of the following paths:(a) Constant volume;(b) Constant temperature;(c)
One mole of an ideal gas with CP = (5/2)R and CV = (3/2)R expands from P1 = 6 bar and T1 = 800 K to P2 = 1 bar by each of the following paths:(a) Constant volume(b) Constant temperature(c)
The state of an ideal gas with CP = (5/2)R is changed from P = 1 bar and V1t  = 12 m3 to P2 = 12 bar and V2t  = 1 m3 by the following mechanically reversible processes:(a) Isothermal
The environmental lapse rate dT/dz characterizes the local variation of temperature with elevation in the earth’s atmosphere. Atmospheric pressure varies with elevation according to the hydrostatic
Gas at constant T and P is contained in a supply line connected through a valve to a closed tank containing the same gas at a lower pressure. The valve is opened to allow flow of gas into the tank,
Develop equations that may be solved to give the final temperature of the gas remaining in a tank after the tank has been bled from an initial pressure P1 to a final pressure P2. Known quantities are
One mole of an ideal gas in a closed system, initially at 25°C and 10 bar, is first expanded adiabatically, then heated isochorically to reach a final state of 25°C and= 1 bar. Assuming these
One cubic meter of argon is taken from 1 bar and 25°C to 10 bar and 300°C by each of the following two-step paths. For each path, compute Q, W, ΔU, and ΔH for each step and for the overall
A scheme for finding the internal volume VtB of a gas cylinder consists of the following steps. The cylinder is filled with a gas to a low pressure P1, and connected through a small line and valve to
In addition to heat and work flows, energy can be transferred as light, as in a photovoltaic device (solar cell). The energy content of light depends on both its wavelength (color) and its intensity.
Liquids that boil at relatively low temperatures are often stored as liquids under their vapor pressures, which at ambient temperature can be quite large. Thus, n-butane stored as a liquid/vapor
An incompressible fluid (ρ = constant) is contained in an insulated cylinder fitted with a frictionless piston. Can energy as work be transferred to the fluid? What is the change in internal energy
Electric current is the fundamental SI electrical dimension, with the ampere (A) as its unit. Determine units for the following quantities as combinations of fundamental SI units.(a) Electric
Liquid/vapor saturation pressure Psat is often represented as a function of temperature by the Antoine equation, which can be written in the form:Here, parameters a, b, and c are substance-specific
The SI unit of luminous intensity is the candela (abbreviated cd), which is a primary unit. The derived SI unit of luminous flux is the lumen (abbreviated lm). These are based on the sensitivity of
An absolute pressure gauge is submerged 50 m (1979 inches) below the surface of the ocean and reads P = 6.064 bar. This is P = 2434(inches of H2O), according to the unit conversions built into a
In medical contexts, blood pressure is often given simply as numbers without units.(a) In taking blood pressure, what physical quantity is actually being measured?(b) What are the units in which
The annual average insolation (energy of sunlight per unit area) striking a fixed solar panel in Buffalo, New York, is 200 W ⋅ m−2, while in Phoenix, Arizona, it is 270 W ⋅ m−2. In each
A wind turbine with a rotor diameter of 77m produces 1.5 MW of electrical power at a wind speed of 12 m ⋅ s−1. What fraction of the kinetic energy of the air passing through the turbine is
Following is a list of approximate conversion factors, useful for “back-of-the-envelope” estimates. None of them is exact, but most are accurate to within about ±10%. Use Table A.1 (App. A) to
Consider the following proposal for a decimal calendar. The fundamental unit is the decimal year (Yr), equal to the number of conventional (SI) seconds required for the earth to complete a circuit of
Chemical-plant equipment costs rarely vary in proportion to size. In the simplest case, cost C varies with size S according to the allometric equationThe size exponent β is typically between 0 and
An egg, initially at rest, is dropped onto a concrete surface and breaks. With the egg treated as the system,(a) What is the sign of W?(b) What is the sign of ΔEP?(c) What is ΔEK?(d) What is
An electric hand mixer draws 1.5 amperes at 110 volts. It is used to mix 1 kg of cookie dough for 5 minutes. After mixing, the temperature of the cookie dough is found to have increased by 5°C. If
Comment on the feasibility of cooling your kitchen in the summer by opening the door to the electrically powered refrigerator.
An electric motor runs “hot” under load, owing to internal irreversibilities. It has been suggested that the associated energy loss be minimized by thermally insulating the motor casing. Comment
A wind turbine with a rotor diameter of 40 m produces 90 kW of electrical power when the wind speed is 8 m ⋅ s−1. The density of air impinging on the turbine is 1.2 kg ⋅ m−3. What fraction of
The battery in a laptop computer supplies 11.1 V and has a capacity of 56 W⋅h. In ordinary use, it is discharged after 4 hours. What is the average current drawn by the laptop, and what is the
Suppose that the laptop of Prob. 2.16 is placed in an insulating briefcase with a fully charged battery, but it does not go into “sleep” mode, and the battery discharges as if the laptop were in
A solid body at initial temperature T0 is immersed in a bath of water at initial temperature Tw0. Heat is transferred from the solid to the water at a rate Q̇ = K̇ (Tw – T) , where K is a
A list of common unit operations follows:(a) Single-pipe heat exchanger(b) Double-pipe heat exchanger(c) Pump(d) Gas compressor(e) Gas turbine(f) Throttle valve(g) NozzleDevelop a simplified form of
The Reynolds number Re is a dimensionless group that characterizes the intensity of a flow. For large Re, a flow is turbulent; for small Re, it is laminar. For pipe flow, Re ≡ uρD/μ, where D is
(a) Water flows through the nozzle of a garden hose. Find an expression for m˙ in terms of line pressure P1, ambient pressure P2, inside hose diameter D1, and nozzle outlet diameter D2. Assume
The heating of a home to increase its temperature must be modeled as an open system because expansion of the household air at constant pressure results in leakage of air to the outdoors. Assuming
(a) An incompressible fluid (ρ = constant) flows through a pipe of constant cross-sectional area. If the flow is steady, show that velocity u and volumetric flow rate q are constant.(b) A chemically

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