Question

This problem is (6.20) from a book  "Thermodynamics and Statistical Mechanics An Integrated Approach by M. Scott Shell"

I already did parts (a,b&c), Please answer the last two parts (d&e)

6.20. If placed in very smooth, clean containers, many liquids can be supercooled to
temperatures below their melting points without freezing, such that they remain
in the liquid state. If left long enough, these systems will eventually attain equilib-
rium by spontaneously freezing. However, in the absence of nucleation sites like
dirt or imperfections in the walls of the container, the time required for freezing
can be long enough to permit meaningful investigations of the supercooled state.
Consider the spontaneous freezing of supercooled liquid water. For this prob
lem you will need the following data taken at atmospheric pressure: cp 38 J/K
mol for ice (at 0 °C, but relatively constant over a small T range); Cp-75 J/K mol
for liquid water (at 0 °C, but relatively constant); and Δhm-6, 026 J/mol for liquid-
ice phase equilibrium at 0 °C. Here Ax indicates iquid Xcrystal for any property x
Recall that E + PV, h = H/N, and Cp = (ah/01),-7(os/OT)P, and that h and s
are state functions
(a) In an isolated system, when freezing finally occurs, does the entropy increase
or decrease? What does this imply in terms of the relative numbers of micro-
states before and after freezing? Is "disorder" a useful qualitative description of
entropy here?
(b) If freezing happens fast enough, to a good approximation the process can be
considered adiabatic. If the entire process also occurs at constant pressure,
how that freezing is a constant-enthalpy (isenthalpic) process
(C) If one mole of
supercooled water is initially at -10 °C (the temperature of a
typical household freezer), what fraction freezes in an adiabatic process as it
comes to equilibrium? Compute the net entropy change associated with this
event. Note that this is not a quasi-static process.
(d) Consider instead the case when the freezing happens at constant T and P.
Under these conditions, explain why the expression Δ:-Δh/T is valid when
liquid water freezes at its melting point, but not when supercooled liquid
water freezes.
(e) Compute ASwater, ASsurw and ASworld when one mole of supercooled liquid
ater spontaneously freezes at -10 °C (e.g, in the freezer). Assume that the
surroundings act as a bath
expand button
Transcribed Image Text:6.20. If placed in very smooth, clean containers, many liquids can be supercooled to temperatures below their melting points without freezing, such that they remain in the liquid state. If left long enough, these systems will eventually attain equilib- rium by spontaneously freezing. However, in the absence of nucleation sites like dirt or imperfections in the walls of the container, the time required for freezing can be long enough to permit meaningful investigations of the supercooled state. Consider the spontaneous freezing of supercooled liquid water. For this prob lem you will need the following data taken at atmospheric pressure: cp 38 J/K mol for ice (at 0 °C, but relatively constant over a small T range); Cp-75 J/K mol for liquid water (at 0 °C, but relatively constant); and Δhm-6, 026 J/mol for liquid- ice phase equilibrium at 0 °C. Here Ax indicates iquid Xcrystal for any property x Recall that E + PV, h = H/N, and Cp = (ah/01),-7(os/OT)P, and that h and s are state functions (a) In an isolated system, when freezing finally occurs, does the entropy increase or decrease? What does this imply in terms of the relative numbers of micro- states before and after freezing? Is "disorder" a useful qualitative description of entropy here? (b) If freezing happens fast enough, to a good approximation the process can be considered adiabatic. If the entire process also occurs at constant pressure, how that freezing is a constant-enthalpy (isenthalpic) process (C) If one mole of supercooled water is initially at -10 °C (the temperature of a typical household freezer), what fraction freezes in an adiabatic process as it comes to equilibrium? Compute the net entropy change associated with this event. Note that this is not a quasi-static process. (d) Consider instead the case when the freezing happens at constant T and P. Under these conditions, explain why the expression Δ:-Δh/T is valid when liquid water freezes at its melting point, but not when supercooled liquid water freezes. (e) Compute ASwater, ASsurw and ASworld when one mole of supercooled liquid ater spontaneously freezes at -10 °C (e.g, in the freezer). Assume that the surroundings act as a bath
Expert Solution

Want to see the full answer?

Check out a sample Q&A here
Blurred answer
Students who’ve seen this question also like:
Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN: 9781259696527
Author: J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher: McGraw-Hill Education
Not helpful? See similar books
marketing sidebar icon
Want to see this answer and more?
Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*
*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.

Related Chemical Engineering Q&A

Find answers to questions asked by students like you.

Q: This problem is (6.20) from a book  "Thermodynamics and Statistical Mechanics An Integrated Approach...

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question...

Q: (a) If 300 lb of air and 24.0 lb of carbon are fed to a reactor at 600 ° and after complete combusti...

A: Part (a)Moles of Carbon fed to the reactor is written as equation (1).Moles of Air fed to the reacto...

Q: A rectangular steel (k = 58.7 W/m * K) fin 25 mm thick and 150 mm long is attached to a wall that is...

A: Part (a)The figure representing the given question is:Let the depth of the fin be 1m as the calculat...

Q: This problem is (6.13) from a book  "Thermodynamics and Statistical Mechanics An Integrated Approach...

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question...

Q: 4.8 A surge tank in Fig. E4.8 is designed with a slotted weir so that the outflow rate, w, is propor...

A: Apply material balance on the given system as:

Q: 38. Following is a labeled flowchart for a steady-state two-unit process, with boundaries shown to d...

A: In the given flowchart, the outer boundary encompasses the entire process. Thus, it gives the overal...

Q: Homework #1 1.18 Nitrogen gas can be injected into oil wells to increase the recovery of crude oil (...

A: Part (a)Note: As the table 1.2 and 1.3 was not provided with the question so, conventional symbols a...

Q: 1. Consider the following reaction sequence: k1 k3 ks k2 Develop a suitable rate expression for prod...

A: Part (a)Michaelis-Menten approach Write the rate expression for the first step for forward and backw...

Q: A mixture of ideal gases has the following composition by mass :Oxygen(60%), Carbon dioxide(20%),Nit...

A: We can calculate the Characteristic gas constant for mixture of gasses by using the following formul...

Q: How much heat (in kJ/hr) is released/absorbed (specify which) if 100 mol/hr of liquid n-heptane is c...

A: The combustion reaction of n-heptane is:

Q: A graphite heat exchanger is constructed by drilling circular channels in a solid block of graphite....

A: Answer:For such type of problem where the other material(graphite) is trapped between two channels, ...

Q: The density of a particular fluid is given by the following equation:where rho = 64e^((7.9x10^-7)P) ...

A: part (a)Since exponential term is dimensionless hence units of 7.9x10^-7 is in^2/lbf as shown below ...

Q: A 4-in. schedule 80 steel pipe (ID = 3.826 in., OD = 4.5 in.) carries a heat-transfer fluid at 600 F...

A: The schematic diagram of the pipe with insulation is given below with the inner radius R1, Outer rad...

Q: This problem is (7.16) from a book  "Thermodynamics and Statistical Mechanics An Integrated Approach...

A: Number of liquid molecules present in the pot is N.Let the number of moles of liquid be n. It is def...

Q: The density of gold is 19.3 g/cm^3 . A 6. 4 mg piece of gold is hammered into a square that is 8.6x...

A: Part (a):The thickness of gold which is hammered into square is given in centimeters as: 8.6*10-6 cm...

Q: A typical column is shown in figure together with the known information for each stream. Calculate t...

A: Let the basis of the process be taken as 100 kg feed (F). Apply material balance on the overall proc...

Q: 

A: Part (a)Let the mass of the fermenter products be mF kg which is fed to the distiller to produce mD ...

Q: 3. Irreversible consecutive reactions A-Boccur in a jacketed, stirred-tank reactor as shown in Fig. ...

A: Let,V be the volume of the tank.ρi be the density of the inlet stream.Ci be the heat capacity of the...

Q: 1:02 AM ll Verizon 99%- Done 4. The enthalpy of vaporization of water at 100 °C is 2256.9 kJ/Kg. Ass...

A: Watson equation is to be used as written below. Here, ΔH1 is enthalpy of vaporization at T1.ΔH2 is e...

Q: Wet towels at the Biltmore Hotel are dried in a continuous dryer after washing for use by hotel gues...

A: Let the basis of the calculation for the given process be 850 kg/day of the dry towels. Water is rep...

Q: Please show all steps, thank you

A: Part (a)Use the Lineweaver Burke plot to determine the value of Vmax (or rmax) and Km at 30°C and en...

Q: This problem is (6.30) from a book  "Thermodynamics and Statistical Mechanics An Integrated Approach...

A: The information provided in the question is as follows:Inside diameter of the hose is d1 = 5 cmNozzl...

Q: PLease show all steps

A: The reaction taking place is, S→P According to the Michaelis-Menten equation, the reaction rate for ...

Q: B C and D ONLY!!!!!!!!!!!!!!!!!!!

A: Part (b)Apply component material balance on the given system for tank 1 and label it as equation (1)...

Q: Cyclohexanol is a highly desired chemical precursor for the production of nylon (billions of kilogra...

A: Part (c)The Antoine equation to be used is written below.Here, Pi* is the vapor pressure of the comp...

Q: 4.2 Consider the following transfer function: Y(s) 3e- U(s) 1Os +1 (a) What is the steady-state gain...

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question...

Q: A small steam superheater will be made of 0.75-in. schedule 80 stainless steel pipe which will be ex...

A: The following conditions are given in the question:

Q: 100 lbm/h of oil at 130F is needed for a process modification. The oil will be available at 70F, so ...

A: Oil is available at 70°F flowing at the rate of 130 lbm/h. It is required to heat the oil to 130°F. ...

Q: The surface temperature of the electronic chip shown below is 75C and it is surrounded by ambient a...

A: The area of the upper surface of the chip carrier is calculated as:

Q: Please show all steps, thank you

A: AnswerPart a:Multiple stAnswerPart a:Multiple states are possible if enzymatic reaction is mass tran...

Q: Uric acid (UA) is degraded by uricase enzyme immobilized in porous Ca-alginate beads. Experiments co...

A: a)From units of rate in the given data (mg/L*hr), the reaction is first order and for the first orde...

Q: This problem is (6.10) from a book  "Thermodynamics and Statistical Mechanics An Integrated Approach...

A: Part (a): Given that the container is well insulated, N moles of a monoatomic ideal gas expands irre...

Q: should not exceeu 120 sho that is described by the Peng-Robinson equa- te, how low a pressure is all...

A: Let the initial conditions be denoted by “1” and final conditions by “2”. The given conditions are: ...

Q: In certain composition ranges of mixtures of ethylene tetrachloride (C2Cl4), isopropyl alcohol, and ...

A: Part (a)The basis of the calculation is taken as 100 lbs of feed mixture containing 40 mass% C2Cl4, ...

Q: details in photo, please show all steps

A: Part (a):Michaelis-Menten approach is best known approach to enzyme kinetics. The given mechanism is...

Q: 

A: Dear student, we provide answers to three parts in a question. So, we are providing answers to first...

Q: A new engineering graduate was putin charge of a reactor. The engineer quickly learned that the proc...

A: Part (b)The Schematic diagram of the given process is drawn below. The basis of the calculation is t...

Q: A novice manufacture of alcohol for gasohol is having a bit difficulty with a distillation column. T...

A: It is given that the weight of the product (distillate) is 1/10 of the feed. Thus,

Q: Some liquid acetaldehyde (C2H4O) is put into a 5L flask. All of the air is removed before the flask ...

A: In a closed system containing one component, when a vapor is in the thermodynamic equilibrium with i...

Q: In

A: Part (a) The reversible reaction for the formation of ammonia from nitrogen and hydrogen is:N2 + 3H2...

Q: To evaluate the use of renewable resources, an experiment was carried out with rice hulls. After pyr...

A: Part (a)The schematic diagram of the given process is shown below.Let the basis of the calculation b...

Q: 2. The liquid-vapor equilibrium of a mixture of toluene (boiling point Of 110.6 °C at 1 atm) and o-x...

A: A mixture of 2 moles of Toluene and 3 moles of o-xylene is given.(a) To calculate the dew point and ...

Q: 2. A jacketed vessel is used to cool a process stream as shown in Fig. E2.The (i) The volume of liqu...

A: Click to see the answer

Q: This problem is (7.6) from a book  "Thermodynamics and Statistical Mechanics An Integrated Approach ...

A: For a single-component system, that is, pure species, the terms fugacity represented by f  is introd...

Q: 5.10. Find the fundamental equation for the intensive quantity eˆ = E/V in differential form. Also g...

A: Step 1:Thanks for the question. We accepted this question by mistake. In the question, the variables...

Q: This problem is (9.19) from a book  "Thermodynamics and Statistical Mechanics An Integrated Approach...

A: The equation of the state of a certain gas is given by equation (1), where,T represents temperature ...

Q: The T-x-y and P-x-y diagrams for the binary benzene-toluene system is shown below. a. The bubble poi...

A: Part (c)The Antoine equation to be used is written below.Here, Pi* is the vapor pressure of the comp...

Q: 1. A closed stirred-tank reactor with two compartments is shown in Fig. El. The basic idea s to feed...

A: Assumptions:Let the heat capacity of the component be represented by C and be constant.Let the densi...

Q: Fuels for motor vehicles other than gasoline are being eyed because they generate lower levels of po...

A: Combustion reaction of propane with air is written as:Note that in the question CO2 and CO are given...

Q: Diesel exhaust fuel (DEF) is a mixture of Urea (CH4N2O) and water (H2O). Often the urea in DEF is ma...

A: Let the basis of the calculation be 1 gallon of DEF (urea + water). Density of DEF is given as 9.1 l...

Knowledge Booster
Chemical Engineering
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemical-engineering and related others by exploring similar questions and additional content below.
Recommended textbooks for you
  • Introduction to Chemical Engineering Thermodynami...
    Chemical Engineering
    ISBN:9781259696527
    Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
    Publisher:McGraw-Hill Education
    Elementary Principles of Chemical Processes, Bind...
    Chemical Engineering
    ISBN:9781118431221
    Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
    Publisher:WILEY
    Elements of Chemical Reaction Engineering (5th Ed...
    Chemical Engineering
    ISBN:9780133887518
    Author:H. Scott Fogler
    Publisher:Prentice Hall
  • Process Dynamics and Control, 4e
    Chemical Engineering
    ISBN:9781119285915
    Author:Seborg
    Publisher:WILEY
    Industrial Plastics: Theory and Applications
    Chemical Engineering
    ISBN:9781285061238
    Author:Lokensgard, Erik
    Publisher:Delmar Cengage Learning
    Unit Operations of Chemical Engineering
    Chemical Engineering
    ISBN:9780072848236
    Author:Warren McCabe, Julian C. Smith, Peter Harriott
    Publisher:McGraw-Hill Companies, The
  • Introduction to Chemical Engineering Thermodynami...
    Chemical Engineering
    ISBN:9781259696527
    Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
    Publisher:McGraw-Hill Education
    Elementary Principles of Chemical Processes, Bind...
    Chemical Engineering
    ISBN:9781118431221
    Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
    Publisher:WILEY
    Elements of Chemical Reaction Engineering (5th Ed...
    Chemical Engineering
    ISBN:9780133887518
    Author:H. Scott Fogler
    Publisher:Prentice Hall
    Process Dynamics and Control, 4e
    Chemical Engineering
    ISBN:9781119285915
    Author:Seborg
    Publisher:WILEY
    Industrial Plastics: Theory and Applications
    Chemical Engineering
    ISBN:9781285061238
    Author:Lokensgard, Erik
    Publisher:Delmar Cengage Learning
    Unit Operations of Chemical Engineering
    Chemical Engineering
    ISBN:9780072848236
    Author:Warren McCabe, Julian C. Smith, Peter Harriott
    Publisher:McGraw-Hill Companies, The