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  • Recently Asked Dynamics Questions

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    • Q1:7. (Denbigh, ch. 9) Consider a two-component "regular solution:" RT log 71 = b(p)x2, RT log 72 = b(p)x2, (a) Verify that the activity coefficients satisfy the Gibbs-Duhem equation. (b) Show that Asmix is the same as for an ideal solution, and show that Ahmix = b(p)x1x2, unlike an ideal solution which has Ahmix = 0. b/RT=4 ₡1 Apmix 02 0.4 0.6 0.8 O RT b/RT=2 0.5 b/RT=0 -1.0- b/RT =- 2 02 0.4 0.6 0.8 -0.05- locally unstable b/RT=2.5 Aplmix RT globally unstable -0.15 -0.20 b/RT=2 -0.25 -0.30- b/RT=1.5 Figure 2: Molar Gibb's free energy of mixing versus composition for different values of B = b/RT. Wide range of B = b/RT (top graph); narrower range of B = b/RT closer to stability transition (bottom graph). -0.10 T2 500 480 460 440 T 420 400 Tı 380 360 0.0 0.2 0.4 0.6 0.8 1.0 21 Figure 3: Binary phase diagram showing miscible liquid phase and immiscible solid phase. (c) Calculate the molar Gibbs free energy of mixing Aftmix. A graph Aftmix is provided in figure 2. Show that the boundary of the two-phase region for T, P fixed is 2Bx1(1-21)=1, where B = b/RT. Note that a single phase exists for 2Bx1(1 - 21) < 1; two phases coexist for 2Bx1(1 -21) > 1. 8. (Denbigh ch. 9) Consider a binary mixture that has an azeotrope. Show that T is an extremum (minimum or maximum) under constant pressure conditions and P is an extremum under constant temperature conditions at the azeotrope 21 = y1 (equal vapor and liquid phase compositions). 9. (Denbigh ch. 9) Consider two metals that form an ideal solution (i.e. are completely miscible) in the liquid phase but are completely immiscible in the solid phase, as shown in figure 3. The melting points of the pure phases are T1 and T2; the heats of fusion, Ah1 and Ah2, are constant. (a) Prove that this system forms a minimum melting temperature eutectic point as seen in Figure 2. To do this, show that the slope dT/dx of the solid-liquid phase boundary is negative for small x and and the slope of the phase boundary is positive for large x. (b) For the special case Ah1 = Ah2 = Ah and T1 = T2 =To, show that the eutectic composition and temperature are given by x = 1 2' T = Ah + RTo log 2 AhToSee Answer
    • Q2:Problem 6 (40 points) An underwater vehicle's motion in the yaw plane is described by the following simplified set of linearized equations: L m-Y; -Y. 0 0v Y U (Y-m)U 0 0 v Y U2 uudr -Ný I =- N, 0 0 r NU uv NU ur 00 r = N,s.U2 uuSr r (1.1) 0 0 10 y 1 0 0 U y 0 − 0 0 0 1 0 1 0 0 y 0 Yvdot = - 291.6078; Yrdot = - 16.4006; Mass = 265.3515kg; Nvdot = - 16.4006; Izz = 271.4616kg - m2; Nrdot = - 214.2764; Yuv = - 101.8686; Yur =91.6398; Nuv =- 233.5181; Nur =- 159.2130; Yu2dr = 61.8201; Nu2dr = - 44.6410; In compact form, Equation(1.1) can be written as Mx = Cax+BS, =Cax+ BOrudder where x =[v r y y]' . Equation(1.2) can be expressed in the traditional state space form as A11 A12 0 07 bị b (1.2) *= M-'Cax+M 'BS, = Ax+ Bô rudder 11 A21 A22 0 0 b2 0 1 0 0 A34 x+ 8 (1.3) rudder 0 1 0 0 0 A block diagram of a control system is shown in Figure 1. K Srudder Vemd 4 desired 2 e + 5 + Krp 4 H1(s) 4 H2(s) Figure 1: Schematic of yaw loop control for underwater vehicle (20 points) Compute the transfer functions H1 = rudder (s) i(s) and H2 = Smudder(s) ų(s) in terms of the components of the A and B matrices. Keep in variable form. (25 points) For a specified speed U of 20 knots and commanded yaw, l cmd , of 10 deg, verify that the rudder, Srudder, does not exceed a magnitude of 15 degrees for the following gains: K5 =1, Kwp =0.86,Kmp =- 0.3822. Use Simulink for this purpose and comment on the results and include a plot of the yaw command, the yaw response, and the rudder response on the same set of axes. 2See Answer
    • Q3:. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. A boat is moving to the right with a constant deceleration of 0.9 m/s- when a boy standing on the deck D throws a ball with an initial velocity relative to the deck which is vertical. The ball rises to a maximum height of 6 m above the release point and the boy must step forward a distance d to catch it at the same height as the release point. D Problem 11.125.a - Relative motion of projectile with given acceleration-find distance Determine the distance d. S A boat is moving to the right with a constant deceleration of 0.9 m/s- when a boy standing on the deck D throws a ball with an initial velocity relative to the deck which is vertical. The ball rises to a maximum height of 6 m above the release point and the boy must step forward a distance d to catch it at the same height as the release point. a - -d D ap Problem 11.125.b - Relative motion of projectile with given acceleration-find a relative velocity Determine the relative velocity of the ball with respect to the deck when the ball is caught. The relative velocity of the ball with respect to the deck is m/s ¥ 0 S Next & Conveyor belt A, which forms a 20° angle with the horizontal, moves at a constant speed of 4 ft/s and is used to load an airplane Knowing that a worker tosses duffel bag B with an initial velocity of 2.5 ft/s at an angle of 30° with the horizontal, determine the velocity of the bag relative to the belt as it lands on the belt. VA 20° A (VB)o B 1 30° 1.5 ft The velocity of the bag relative to the belt as it lands on the belt is ....... O ft/s at an angle of: s Required information Problem 11.124 - Relative/dependent motion of particles with given velocities and accelerations- DEPENDENT MULTI-PART PROBLEM ASSIGN ALL PARTS NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. 6 For the system shown, block A has a velocity of 7 in/s and an acceleration of 5 in/s- both directed down the incline. B. 15° A 25° Problem 11.124.b - Relative/dependent motion of particles with given velocities and accelerations-fl acceleration Determine the acceleration of block B. The acceleration of block B is in/s2 at an angle of 0 .See Answer
    • Q4:The Amazon delivery drone A drops a package when the drone has the velocity VA and the acceleration aд shown at t=0. Assume that the wind creates a constant horizontal resistance of 0.1 m/s² on the projectile. Determine at, an and the radius of curvature of the package P when the package drops h=10 m in altitude using (a) vector algebra (dot product), and (b) vector decomposition. Requirement: Set up the x-y frame (axes and the origin) of your choice, and clearly mark it in the problem picture. Your +x can be to the right or to the left. Your +y can be upward or downward. Your origin can be anywhere. It is your choice, but you must show me in order to use any projectile motion equations. Ans: at 8.6231 m/s², an=4.6785 m/s², rho=566.8 m P Wind UA-50% ·AA = 3 m/s² h 60° DSee Answer
    • Q5:Graded HW#3 Ans: (a) 0.5657 in/s, 1.1328 in/s2 (b) 0.0549 rad/s CW, 0.10606 rad/s² CW. (a) A disk cam rotates about its pin connection O at the 9 o'clock position with the angular velocity and angular acceleration at the instant shown. Find the magnitude of the velocity and magnitude of the acceleration of point P at the 12 o'clock position at the instant. If you have trouble visualizing the correct circular motion, cut a disk from a piece of paper and pin down the left edge and turn around. P R=4" Hint: v is tangent to the path of P, not tangent to the shape of the object. What is the radius of the circular path of P? Does P circle around the disk center? Is the "radius" equal to R-4"? Of course not. Which point is the center of the circular motion? W=0.1 rad/s α=0.2 rad/s2 CW (b) The disk cam is controlled by the 5" slotted arm AB through a pin P fixed on the disk. If at the instant shown, 0=60°, =-0.1 rad/s, and = 0.2 rad/s², find the angular velocity @ and the angular acceleration a of the disk at the instant. O is at the 9 o'clock position P is at the 6 o'clock position. Hint: Again, vP is not tangent to the physical shape of the disk. The circular shape is a bait. 本 B R=4"See Answer
    • Q6:HW07_#3 SMOOTH Block A (200 lb) and Block B (350 lb) are constrained by a pulley system and initially at rest. As the ramp is smooth, ignore all friction. Also ignore the mass of the cables and pulleys. A. Find the acceleration of each block B. The tension in the cable C. (circle ONE) If you were to include the mass of the cables and pulley, the system would SLOW DOWN SPEED UP Ans: A: aA = 8.4 ft/s^2 (up to right), aB-4.2 ft/s^2 (down), B: T=152.2 lb 30° 200 lb B 350 lbSee Answer
    • Q7:12-224 (modified) At the instant shown, car A travels along the straight portion of the road with a speed of 25 m/s. At this same instant car B travels along the circular portion of the road with a speed of 15 m/s. Determine the velocity of car B relative to car A. B. Sketch the velocity vector from your answer C. Visualize and explain what the velocity of car B relative to car A would look like if you were sitting in Car A. D. If car A is slowing down at 2 m/s² and car B is moving at a constant velocity, what is the acceleration vector of car B relative to car A in horizontal and vertical components. To help clarify the geometry: Car A lies on line AC which is 30° from horizontal. Car B is only 15 degrees from horizontal (as its half-way around a 30° curve) Ans: A. VB/A=< -7.162, 8.618 > m/s D. ab/A=< 2.023, 0.087 > m/s² UND ما 15° p = 200 m 30° B -15°See Answer
    • Q8:HW06_#3 4-Pulley A 4-pulley system is used to lift up block A at 1 ft/s. What is the required velocity of block F? Ans: 15 ft/s downward too A E FSee Answer
    • Q9:HW06-#2 H₂O SKIER A water skier angles her skis to create a 0 = 30° angle between her r=10m (fixed length) tow rope and the boat (VB = 60 km/hr). At this instant, the heading of the skier makes an angle of ß = 50° with the tow rope. Assume the water in the lake is stationary. Find: A. The velocity equation relating the skier to the boat, including both absolute and relative terms. The velocity of the skier S relative to the water (in km/hr) B. B C. The angular velocity of the rope relative to the boat (d0/dt or w) in rad/s. For fixed radius (circular) motion like this v = r de/dt. km km Ans: Vs = 80.8- hrVS/B = 31.93m, w = 0.89² hr rad S UB 0 B 10 mSee Answer
    • Q10:12-229. Cars A and B are traveling around the circular race track. At the instant shown, A has a speed of 90 ft/s and is increasing its speed at the rate of 15 ft/s², whereas B has a speed of 105 ft/s and is decreasing its speed at 25 ft/s². Determine the relative velocity and relative acceleration of car A with respect to car B at this instant. A. Express both vectors as x,y vector components. Ans: VA VA (x,y) = (-37.5,-90.93), (x,y) = (10.69, 16.7) S A = 300 ft 60⁰° TB=250 ftSee Answer
    • Q11: MECH 1215 LABORATORY THREE (WEEK 16) ADIABATIC COMPRESSION LAB OBJECTIVE 1. On completion of the laboratory the students will have familiarised themselves with polytropic processes, in particular adiabatic and isothermal compressions, and how to experimentally determine the polytropic index from Equation 1. PV = C₁ Thermodynamics lab 2 Where P is the pressure, V is the volume, n is a constant (the polytropic index) that defines the behaviour of the compression process and c, is some constant. 2. STRUCTURE Students will work in groups of 3 or 4, depending on laboratory group size on the day, and each group will carry out up to three (3) repeat experiments for both (1) adiabatic and (2) isothermal compression experiments. However, each student will use the data generated individually. [1] Note 1: You are expected to run each experiments multiple times (a minimum of 3 repeats of each of isothermal and adiabatic compression experiments is required. More is better). Isothermal compression Adiabatic compression (or as close to this as possible) In particular the students will be required to find the value of n for air under conditions of MECH1215: Thermofluids 1 You are expected to find these values within the 2 hour lab session, using a combination of experimentation, mathematical manipulation of equations and data-processing with either excel or MatLab. Once you have found values for n, there is a supplemental question to answer. Details in the sections detailing the tasks to be be undertaken in as part of this lab processes. Laboratory 3 Page 1 of 10 MECH 1215 Introducing ReLOAD Protocol ReLOAD Protocol has been been introduced to the lab this year. This will be used in generation and collation of experimental data. There is also an opportunity for you to use the ReLOAD user interface to evaluate the correctness of your data, particularly you estimated values of polytropic index “n”. Details of the implementation of the ReLOAD protocol is provided in the section on Experiment methodology. 3. DELIVERABLES Thermodynamics lab 2 Each student is required to submit one lab report covering the experiment which should be concise and accurate. Maximum length: 10 pages (excluding cover and reference pages) Important note - Each report should have: Introduction: Putting the work into context and describing the background theory. The introduction should start with some background to the experiment, applications in the real world and relevance of the experiments you are about to undertake. Introduce the appropriate equations and explain the assumptions behind them, their limitations and again relate this to real systems. Aim/Objectives: Explain what your hope to achieve from the lab practical. All aims and objectives should be mentioned. Apparatus A list of the apparatus used and a diagram of the experimental system, with proper labels showing each part/component with a brief description of the function of each (Hand drawing diagrams should be avoided). Methodology: Providing enough information to enable someone to repeat the measurements themselves to the same degree of accuracy. It should have the settings used on any equipment and what controls were in place such as room temperature, placement of equipment, data processing, etc. MECH1215: Thermofluids 1 Laboratory 3 Page 2 of 10 MECH 1215 Results: Conclusions: In a concise form for each task, with the important data clearly highlighted, with no room for interpretation, example calculations provided and all questions within that task answered. Any post- processing of data, curve fitting, figures/plots should be presented and fully described. A description of your data analysis procedure (including any mathematical derivations). Must include graphs and fitted expressions to give n and work for the different scenarios. The results must show repeatability with error bars use to demonstrate this. This will mean that a minimum of two (3) repeats of test is carried out with all measurements recorded. Discussion: Containing an analysis and interpretation of the results based on the information collected and explaining its significance. Identify important issues, discuss the accuracy of the results and explain your findings. Compare your results with theoretical values and standard values from literature (i.e. lecture notes, books, scientific papers). Concise list of the conclusions arising from each experiment. No new information should be contained within this section. References Citations to appropriate literature must be included. Thermodynamics lab 2 Please follow Library referencing guidelines for references and citations: https://library.leeds.ac.uk/info/1402/referencing. The School of Mechanical Engineering follows Leeds Harvard or Leeds Numeric. Select one of these styles and be consistent throughout the report. Formatting exactly as per the guidelines. Please note: Experiments can be done as a group to generate data. The laboratory support staff on ground will guide you on the exact format for this. So please follow their lead. Data processing and report writing MUST be done individually. You are advised to bring your own laptop. This is to allow you start processing your data individually once you have generated your data. You can then be able to ask for further guidance from the support staff around. MECH1215: Thermofluids 1 Laboratory 3 Page 3 of 10 MECH 1215 ● When reporting data, please ensure you use the correct number of decimal places, ensure consistent number of decimal places, and add appropriate labels and units in every plot. All graphs, diagrams and images should be labelled as Figure followed by a number and caption. Do not use Picture 1 for example. Tables should be labelled as Table 1 etc. (It is not necessary to include a graph title when an appropriate figure caption is used and placed underneath the graph). Thermodynamics lab 2 Each section listed in the lab handout must have its own section header and be clearly distinguished from the other sections. Please order the report as per the lab handout. Marks will be awarded for presentation of figures, equations and tables. A Laboratory report should be written in 3rd person, mainly in the present tense. Past tense should only be used when describing the work carried out and the results obtained. Format the document appropriately. Do not provide a report where each task is answered one after another throughout the document. The report should be submitted electronically as per the instructions on Minerva. Standard University penalties will be applied to work handed in after the deadline without mitigating circumstances. MECH1215: Thermofluids 1 Laboratory 3 Page 4 of 10 MECH 1215 Experiment Methodology Adiabatic Gas Law Apparatus You will be provided the apparatus showed bellow. It consists of a piston within a cylinder and mechanical parts to allow a rapid compression, together with the following instrumentation: A pressure probe A temperature probe A position gauge The output signals are fed into a data logger connected to a computer. Arduino software is used to run a suitable programme to acquire the data. ReLOAD is used to provide an interactive platform for running the experiments and collation of generated data. ReLOAD Protocol Thermodynamics lab 2 Note that these task are here to help you work through the laboratory session. The tasks should not form the basis of the structure of the laboratory report i.e. DO NOT write a report which is itemised task 1, task 2 etc. with responses to each individual task. Instead incorporate the work appropriately into the methodology, results and discussion section where suitable. Each of the adaibaitic compression apparatus is assigned a unique number (1 – 8) on ReLOAD. Student MUST check that the number on the compression apparatus to identify the same number on ReLOAD. MECH1215: Thermofluids 1 All students should now have a loggin to ReLOAD from using ReLOAD as part of MECH1010. Laboratory 3 Page 5 of 10See Answer
    • Q12:Problem 1: Normal-butane is stored in a steel tank and the temperature of the tank and butane inside is kept at a constant temperature T = 85°F Use these parameters for your calculation. Acentric factor w = 0.193, critical temperature Tc = 305.62°F, critical pressure pc = 550.6 psia, Vc = 4.1 ft³/lbmol. a) Use Lee-Kesler's correlation to calculate the n-butane vapor pressure inside the canister. (5 points) b) Write down the van der Waals EOS and calculate the constants a, b using the critical properties given above. Use n = 1 pound-mole, or Ibmol. (5 points) c) Calculate the critical volumes Vc, ft³/lbmol, from VDW EOS. Compared the calculated Vc and the given value. (5 points) d) Plot pressure p vs. volume V for one Ibmol of butane gas. Use Vmin = b + 0.2, V₁ = 1.02Vmin, V₂ = 1.02V₁, V3 = 1.02V₂, ... until Vmax > 150 ft³. (10 points) a) Using VDW EOS b) Using the Ideal Gas EOS e) Use the calculated vapor pressure, and p vs. V plot to estimate the system volumes at the dew point and bubble point, respectively. (5 points)See Answer
    • Q13: SCHOOL OF ENGINEERING Year 2 Laboratories HPR Heat Pump/Refrigeration Cycle Lab MECH217: Thermodynamics Notation Symbol C COP COPR CoPHP H р Pin Pout P Qin Qout lc Qn RPM Tort Tc Th Tin Tout Tshaft Win W C g h mR mw S u Z ne 3 Meaning Specific heat of water Coefficient of Performance Coefficient of performance or refrigerator Coefficient of performance of heat pump. Enthalpy Pressure Pressure before throttle Pressure after throttle Power Heat into the system Heat out of the system Heat transfer rate in evaporator Heat transfer rate in condenser Revolutions per minute of compressor shaft Temperature Temperature of heat source Temperature of heat sink Water coolant inlet temperature Water coolant outlet temperature Torque on compressor shaft Work into system Work Speed of fluid Gravitational constant Specific enthalpy Mass flow rate of refrigerant Mass flow rate of water Specific entropy Specific internal energy Position along the vertical axis Isentropic efficiency of compressor Angular velocity of compressor shaft Unit J/kgK J Pa Pa Pa J/s J J J/s J/s K K K K K Nm J/s J m/s m/s² J/kg kg/s kg/s J/kgK J/kg m rad/s Abbreviations BDC HP R TDC 1 Introduction In thermodynamics we are commonly interested in the conversion of thermal to mechanical energy. The analysis of these conversion systems often involves thermodynamic cycles. Another important branch of thermodynamics is concerned with the conversion of mechanical to thermal energy and this takes place in reverse cycles. These systems are commonly known as refrigeration systems. Bottom dead centre Heat pump Refrigerator Top dead centre The Second Law of Thermodynamics states that, 'it is impossible to transfer heat from a region of low temperature to a region of high temperature without the aid of some external agency'. Heat pumps and refrigerators are devices that enable heat transfer to take place from a region of low temperature to one of high temperature, the external agency being compressor work in a vapour compression cycle (Win), see Figure 1. The refrigerator is a device for removing heat from a low temperature region. Its coefficient of performance, COPR is defined as the refrigeration rate (or duty) divided by the power input. The heat pump is a device whose prime duty is the delivery of heat to a higher temperature region. Its coefficient of performance CoPHP is defined as the rate at which heat is delivered divided by the power input. ● To avoid ambiguity, the power on which the above definitions for CoP are based must be clearly stated. The power may be: The electrical power required to drive the motor. The increase in enthalpy across the compressor The theoretical power of an ideal compressor. It is important to state clearly which method of energy measurement is being used. The equations to calculate the CoPs will be discussed in more detail in Section 2. 1.1 Background 1.1.1 The Vapour Compression Cycle As discussed in the thermodynamics lecture course, refrigerators and heat pumps operate on reversed vapour compression cycles, i.e. the working fluid (refrigerant) flows around the cycle in the opposite direction to that in a Heat Engine. The simplest thermodynamic cycle is the Ideal Vapour Compression Cycle shown in Figure 2 and Figure 3. Starting at the compressor inlet (1), with reference to Figure 2 and Figure 3, the saturated vapour refrigerant is compressed from a low pressure to a higher one and exits at (2). The high pressure and temperature (relatively) vapour enters the condenser at (2) and passes the condenser through where it gives up its heat and changes from a superheated vapour to a saturated liquid. The refrigerant exits the condenser at (3). The high pressure saturated liquid enters the throttle at (3), and is then expanded with constant enthalpy (no work or heat transfer) to a lower pressure and exiting the throttle at (4). Ambient R Cold Refrigerated Space 3 QH Throttle W in Warm Sink. TH QH Condenser Refrigerator Heat Pump Figure 1: Schematic of heat pump and refrigeration plant This is done so that a portion of the liquid evaporates causing the refrigerant to become colder due to part of its internal energy being used to provide the latent heat of vaporisation. The refrigerant then repeats the cycle when it enters the evaporator at (4), where the heat is transferred from the cold source and the refrigerant changes from a gas/liquid mixture to a saturated vapour. The terms 'condenser' and 'evaporator' are recognisable from their counterparts in a steam power cycle and are the technical terms used in refrigeration; it can be seen however that the evaporator is at the lower temperature in the cycle, and the condenser is at the higher. The energy transfers, as either heat or work, over the different process are listed below. It is important for the student to understand the direction of the energy transfer, so as to be able to make 'sanity checks' on the results. Evaporator Warm Space (e.g. house) 41 Heat transfer from a 'cold' source to refrigerant 12 Work done on fluid during compression 2 → 3 Heat transfer from refrigerant to a 'hot' sink in the condenser 3 →4 A constant enthalpy throttling process QH The Ideal Vapour Compression Cycle is characterised by the refrigerant entering the throttle as a saturated liquid, entering the compressor as a saturated vapour, and an isentropic compression process (reversible and adiabatic). It is also assumed there are no additional heat losses/gains around the cycle and no pressure losses. Qc Cold -Source. Te HP Qc 2 Constant Compressor Enthalpy EFTER 3 Cool/warm Source 1 Win Figure 2: The ideal vapour compression cycle 4 QH Гос 2 1 Win Entropy s Pressure p ● ● 3 Win Figure 3: Pressure - Enthalpy diagram for the ideal vapour cycle It is more convenient and normal practice to represent the cycle on a pressure vs. enthalpy (p-h) diagram as shown in figure 3. Showing the cycle this way makes it easy to see the energy transfers (Q, W). 4 Qc 3 QH 4 1.1.2 Practical vapour cycle The ideal vapour cycle is not a practical cycle for the following reasons: Compression is neither adiabatic nor reversible (non-isentropic). Vapour leaving the evaporator is usually made slightly superheated. Liquid leaving the condenser is usually slightly sub-cooled. 1.2 Aims and Objectives The objectives of the experiment are as follows: Subcooling at Throttle inlet 1 2 Figure 4 shows the p-h diagram for the practical cycle. A higher heat input and output found in practical vapour cycles, is shown on the graph as longer horizontal lines for processes 4-1 and 2-3. It also results in a higher work input, which reduces the CoP of the cycle. Constant Entropy The refrigerant is sub cooled in the condenser to make sure that the refrigerant has become completely fluid. Similarly, the refrigerant is superheated in the evaporator to make sure it is all gas. Refrigerant going into the compressor as part liquid and part gas, would damage the compressor. 1 Enthalpy h 2s 2 Non-isentropic compression Superheat at Compressor inlet Figure 4 Practical vapour cycle plotted on a p-h diagramSee Answer
    • Q14:Lecture 16: Equilibrium of Multiple Condensable Vapors Problem 6: A tank is filled with propane C₂H₂, the first component, and n-hexane CH₁4, the second component. For a constant temperature, there exist both liquid and vapor phases inside the tank, and the liquid and vapor are in equilibrium. The measured vapor composition is y₁ = 0.925008, y₂ = 0.074992, liquid composition x₁ = 0.243423, x₂ = 0.756577. The total mass inside the container is 5 moles, and the 3.851377 moles are in the liquid phase. 1. Calculate the equilibrium constants K₁, K₂ (3 points) 2. Calculate the moles of propane and n-hexane in the vapor phase, 1v1.1v2 (3 points) 3. Calculate the moles of propane and n-hexane in the liquid phase, 1₁, 12 (3 points) 4. Next, the system temperature is raised above the critical temperature of n-hexane, and both compounds exist as vapor only. Calculate the composition inside the container. (3 points) Propane + n-Hexane Vapors Propane + n-Hexane LiquidsSee Answer
    • Q15: CHE 120 Homework Assignment Week 8 Lecture 15: Equilibrium of Condensable Vapor and Noncondensable Gas Problem 1: Textbook 8.3.5. (5 points) *8.3.5. Calculate the vapor pressure of each compound listed below at the designated temperature using the Antoine equation and the coefficients in Appendix H. Compare your results with the corresponding values of the vapor pressures obtained from the Antoine equation found in the physical properties package on the CD accompanying this book. a. Acetone at 0°C b. Benzene at 80°F c. Carbon tetrachloride at 300 K CHE 120-Spring 2024-Chang 1 Chemical Engineering Physical Properties Heat Capacities Enthalpies Density of Liquid Vapor Pressure Steam Tables Compounds Miscellaneous AMMONIA ACETONE A-D E-H 1-EICOSANETHIOL AR BR2 CL2 CS2 F2 H2 H20 I-L 1-IODOPROPANE M-Q 1,2-PENTADIENE R-X 1,1,1-TRIFLUOROETHANE Formula CCL4 CCL3F CCL2F2 CCLF3 Acetone at O C CF4 CO CO2 Fomula Vapor Pressure (mmHg) (Tis in ℃) t Max logop*= 7.2316 OK Min Ⓒby David Himmelblau 2000. All rights reserved. ACETONE C3H60 Temperature 0 -32 CHE 120-Spring 2024-Chang p* (mmHg) 1277.03 [T+ 237.23 } 77 ℃ CCF CK 70.552 2 Chemical Engineering Physical Properties Heat Capacities Enthalpies Density of Liquid Vapor Pressure Steam Tables Compounds Miscellaneous AMMONIA BENZENE A-D E-H 1-EICOSANETHIOL AR BR2 CL2 CS2 F2 H2 H20 I-L 1-IODOPROPANE M-Q 1,2-PENTADIENE R-X 1,1,1-TRIFLUOROETHANE Formula CCL4 CCL3F CCL2F2 CCLF3 Benzene at 80 F CF4 CO CO2 Fomula Vapor Pressure (mmHg) (Tis in ℃) t Max logop*= 6.90565 OK Min Ⓒby David Himmelblau 2000. All rights reserved. BENZENE C6H6 Temperature 80 -16 CHE 120-Spring 2024-Chang p* (mmHg) 1211.033 (T+ 220.79 } 104 ℃ CC OF CK 102.738 3 Chemical Engineering Physical Properties Heat Capacities Enthalpies Density of Liquid Vapor Pressure Steam Tables Compounds Miscellaneous AMMONIA A-D CARBON-TETRACHLORIDE E-H 1-EICOSANETHIOL I-L 1-IODOPROPANE AR BR2 CL2 CS2 F2 H2 H20 M-Q 1,2-PENTADIENE R-X 1,1,1-TRIFLUOROETHANE Formula CCL4 CCL3F CCL2F2 CCLF3 Carbon-Tetrachloride at 300 K CF4 CO CO2 Fomula Vapor Pressure (mmHg) (Tis in ℃) t Max OK CARBON-TETRACHLORIDE Min logop*= 6.8941 Ⓒby David Himmelblau 2000. All rights reserved. CCL4 Temperature 300 -20 CHE 120-Spring 2024-Chang 1219.58 p* (mmHg) 101 (T+227.17 CC CF K 123.875 t ] 4See Answer
    • Q16:Problem 1-10 points Add the following instrumentation to the process flow diagram shown below. Use ISA notation and show all instruments using unique tag numbers. Use pneumatic control valves. All transmitters should be electronic. Assume we are using a DCS with LCD operator consoles. Required instrumentation: a) Local temperature indicators on the inlet and outlet streams to the furnace and the outlet of the reactor. Local pressure indicators on the inlet and outlet of the pump and the inlet of the reactor. A feedback control loop to control the temperature of the outlet stream from the b) c) d) e) furnace. Identify the CV-MV pairing. A back-pressure control loop on the reactor outlet stream. Identify the CV-MV pairing. All of the required instrumentation to monitor the furnace stack temperature on the operator's console in the control room including a separate high temperature panel alarm.See Answer
    • Q17:respectively. 35% and 90%, (33.3%) 5. Consider a simple Rankine cycle with the following operating with a condenser exit temperature of 44°C, a boiler exit pressure of 30 bar, a maximal temperature of 600°C, and a mass flow rate of 40 kg/s. a. Determine the power output produced by this cycle. (52.47 MW) b. Assuming a cooling water, entering at a temperature of 10°C and leaving at 17°C, is used to condensate the steam in the condenser, determine the required mass flow rate for this cooling water. Assume Cp (cooling water) = 4.187 kJ/kg K. (2980.10 kg/s)See Answer
    • Q18:temperature of 500°C. 4. Determine the thermal efficiency of the simple Rankine cycle in question 3, knowing (37%) that the isentropic efficiencies of the pump and the turbine are 85% and 90%, respectively. (33.3%) 5. Consider a simple Rankine cycle with the following operating with a condoncor quitSee Answer
    • Q19:1-s axes and describe each individual process in the cycle. 2. Using the steam tables provided, find the following fluid properties: a. The specific volume of saturated liquid water a temperature of 90 Celcius. b. The specific enthalpy of saturated liquid water at a pressure of 10 bar. c. The specific enthalpy change of vapourisation of water at atmospheric pressure. d. The specific entropy of liquid water at a temperature of 56 Celcius. e. The specific enthalpy of superheated steam at a pressure of 50 bar and a temperature of 800 Celcius. f. The specific entropy of superheated steam at a pressure of 25 bar and a temperature of 500 Celcius. 3. Determine the thermal efficiency of a simple RankinSee Answer
    • Q20:1. Draw a schematic of a power plant that runs on the ideal Rankine cycle. Also draw the Rankine cycle on T-s axes and describe each individual process in the cycle. 2. Using the steam tables provided, find the following fluid proportioSee Answer
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