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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: 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
Q3: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
Q4: 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
Q5: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
Q6: 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
Q7: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
Q8: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
Q9:1-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
Q10:1. 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
Q11: Exercises chapter 001. Volume / specific volume 1.1 Plotting Vapour Pressure So that you get used to the different properties, we are going to spend some time plotting them and commenting on them. (a) You are to begin by plotting the vapour pressure of water against temperature. You need the first steam table for this. (b) You already know that ‘water boils at 100 °C'. Does this graph agree with your experience? 2.0 р MPa 1.5 Sol.: In class. 1.0 0.5 T 0.0 0 100 200 °C university of groningen CHTT-09. Technische thermodynamica / 1 1.2 Volume versus Pressure Your second assignment: find all the data that you can on the volume of both steam and water at a temperature of 200 °C. You will need data on 'saturated' steam and water, on 'superheated' steam and on compressed water. Plot these data in the logarithmic graph below and answer the following questions: (a) You will find that the vapour volume decreases with increasing pressure. The slope of the line is -1; what does this mean? Remember that we are plotting the logarithm of volume against the logarithm of pressure. (b) What can you say about the effect of pressure on liquid volume? (c) The line of the gas volumes has an abrupt step connection to the line of liquid volumes. At which pressure does this occur? Sol. In class. 10 m³ kg 1 0.1 T=200°C 0.01 р MPa 0.001 0.01 0.1 1 10 university of groningen CHTT-09. Technische thermodynamica / 2 1.3 Volume versus Temperature (1) Plot the volumes of liquid against temperature in the upper diagram. The pressure is 5 MPa. What do you see for temperatures up to 100 °C? (2) Plot the volume of the gas against temperature in the lower diagram. The pressure is 0.1 MPa What does the slope in the graph for the gas indicate? liquid at p=5MPa 0.001 0 m³ kg¹ T °C 0.000 0 100 Sol.: In class. 10 vapour at p=0.1MPa D 3 m² kg‍ T K 1 100 1000 university of groningen CHTT-09. Technische thermodynamica / 3 1.4 Volume near the Critical Point Your last plotting exercise. Do note that both scales in this logarithmic diagram have been shifted by a factor of ten compared with that in exercise 1.2. You are to plot the following: the critical point volume of the saturated vapour and of the saturated liquid volume of the (superheated) vapour at 300 °C and at 400 °C volume of the (compressed) liquid at 300 °C. 1 U 3 m³ kg³¹ 0.1 0.01 0.001 Sol.: In class. р MPa 0.1 1 10 100 university of groningen CHTT-09. Technische thermodynamica / 4 1.5 Piping at Home A suitable velocity for a liquid in a pipe is 1 m s-¹. For gases higher velocities are applied, say 10 m s-¹. Using these values calculate the inner diameters of pipes required for the following purposes: (a) Filling the flushing tank of a toilet. This requires about 6 L in one minute. (b) For the forced ventilation of the house. This amounts to about one house volume per hour, say 360 m³ h-¹. Sol.: (a) 1.1 cm; (b) 11.3 cm. 1.6 Large Flows Flows in technical systems can be much larger than in the household. Two examples: (a) Suppose you need to drain an area of one square kilometre. The heaviest rainfall expected is 1 cm h-¹. Which diameter ‘sewage pipe' would you need if the velocity in the pipe is 1 m S-¹? (b) A gas-fired power station might burn 100 m³ s-¹ of natural gas. This requires about 1000 m³ s-¹ of ambient air for combustion. (We study this in more detail in Lesson 10). This air leaves the installation at a temperature of 450 K and ambient pressure (0.1 MPa). The velocity in the stack (chimney) is 15 m s¹. What is the required stack diameter. (You may find the result surprising.) Sol.: (a) 1.9 m; (b) 11.3 m 1.7 Gas Pipeline The main pipes of the National Gas Company have a diameter of 1.2 m. They are operated under a pressure of 8 MPa, with a gas velocity of 5 m s-¹. You may assume a pipe temperature of 290 K. How many moles of gas (methane CH4) are transported per second? The gas constant has a value of 8.314 J mol‍¹ K-¹. Sol.: 1.876× 104 mol/s. 1.8 Derivation of the simplified ideal gas law The simplified ideal gas law establishes that pV/T is constant for a closed system. You are asked to derive this expression from the general equation of state: ov dV = ᎧᎢ av dT + ӘР dP P Taking into account the following historical empirical laws: 1) Boyle-Marriotte: At constant temperature the product pV is constant; 2) Gay-Lussac: At constant pressure the ratio V/T is constant. Sol.: Challenge 1.9 Percentage of error using the ideal gas law What is the percentage of error involved in treating steam as an ideal gas at the following conditions? a) p 1 MPa, T = 400 °C; = b) p = 10 MPa, T = 400 °C. Sol.: a) 1.3 %. b) 17.8 %. university of groningen CHTT-09. Technische thermodynamica / 5See Answer
Q12:The following items must be included in the flowchart: 1. AE=q+w 2. Thermochemical stoichiometry 3. q=mCAT 4. qhot + q cold = 0 5. Bomb calorimetry: qcal = CcalAT 6. Standard enthalpy of formation 7. AH° En AH°(products)- Em AH°(reactants) = 8. Hess's LawSee Answer
Q13:Problem 1: Textbook 9.2.3 Calculate the following quantities using the definition of enthalpy. Assume the air is an ideal gas, the heat capacities c₁ = 21 J/gmol.K, cp=cy + R, where R is the gas constant. Use tank volume V = 10 m³. *9.2.3. A rigid tank contains air at 400 kPa and 600°C. As a result of heat transfer to the surroundings, the temperature and pressure inside the tank drop to 100°C and 200 kPa, respectively. Calculate the work done during this process. a) The total heat transfer AQ in joules (3 points) b) The work done to the system or surroundings AW (3 points) c) The internal energy change AU (3 points) d) The enthalpy change AH (3 points)See Answer
Q14:A sample of natural gas is 87.0% CH4 and 13.0 % C2H6 by mass. What is the heat from the combustion of 3.80 g of this mixture? Assume the products are CO2 (g) and H2O(l). ΔΗ Substance kJ J mol-¹) CH4(g) -74.81 C2H6 (g) -84.86 CO2(g) -393.5 O2(g) 0 H2O(l) -285.8 kj heat is evolved Submit Answer Retry Entire Group 5 more group attempts remainingSee Answer
Q15:A bomb calorimeter, or constant volume calorimeter, is a device often used to determine the heat of combustion of fuels and the energy content of foods. Since the "bomb" itself can absorb energy, a separate experiment is needed to determine the heat capacity of the calorimeter. This is known as calibrating the calorimeter. In the laboratory a student burns a 0.611 g sample of para-benzoquinone (C6H4O2) in a bomb calorimeter containing 1160 g of water. The temperature increases from 25.40°C to 28.10°C. The heat capacity of water is 4.184 J/(g °C). The molar heat of combustion is -2747 kJ per mole of para-benzoquinone. C6H4O2 (s) + 602 (g) →6CO2(g) + 2H2O(l) + Energy Ignition wires Thermometer Stirrer heat sample Water Insulated Sample Burning Steel outside dish sample bomb chamber Previous Next>>/nIgnition wires heat Thermometer Stirrer sample Water Insulated Sample Burning Steel outside dish sample bomb chamber Combustion (bomb) calorimeter. Calculate the heat capacity of the calorimeter. Heat capacity = J/°CSee Answer
Q16:(6 points) 1. If oxygen is in excess, how much heat (q) will 100 grams of C8H18 produce when it is completely consumed? Use the information in the following equation to complete your calculations. 2C8H18 (1) +2502 (g) → 16CO2 (g) + 18H₂O (I), AH = -10,941 kJSee Answer
Q17:(4) A steady flow for refrigerant R134a enters a 35 cm diameter pipe at 200 kPa and 30 °C with a velocity of 6 m/s. The refrigerant is heated along the exterior walls of the pipe via electrical resistive heaters, exiting the pipe at 180 kPa and 60 °C. Note: There was a slight pressure loss due to friction between the fluid flow and the pipe walls. However, in some applications we can assume isobaric operation of the steady flow system. Determine the following, Part A: the volume flow rate of the refrigerant at the inlet Part B: the mass flow rate of the refrigerant through the pipe 1 Part C: using an assumption of constant density, estimate the velocity and volumetric flow rate at the exit. Based on the properties you found at state 1 and state 2, comment on the limitations of this assumption. Q 2 Part D: Calculate the heat flow rate (kW) delivered by the electrical coils assuming 1) the fluid exits at the recorded 180 kPa and 2) the flow remains isobaric through the system. Calculate the percent difference in the calculated heat flow rate between 1 and 2. Describe the impact of the isobaric assumption on the calculated value. Note: do not assume constant density anymore, that was just for part C.See Answer
Q18:Problem 1 (10 points) Using a chemical equilibrium program, such as NASA CEA, determine the adiabatic flame temperatures for the fuels below. Consider equivalence ratios from 0.5 to 1.6 in steps of 0.1 and an unburned temperature of 298.15 K and a pressure of 1 atm. Plot the adiabatic flame temperatures against the equivalence ratio on a single graph with corresponding legend. a) Hydrogen, Methane, Butane, n-heptane, Ethanol Now, obtain the adiabatic flame temperature for propane in the same range of equivalence ratios at: b) an unburned temperature of 298.15 K and a pressure of 1 atm c) an unburned temperature of 450 K and a pressure of 1 atm d) an unburned temperature of 298.15 K and a pressure of 5 atmSee Answer
Q19:Answer the following: Two flash distillation columns are connected together as shown in the following diagram. Both are at 1 atm. The feed to the first drum is a binary mixture of methanol and water of 55 mol % MeOH. Feed flow rate is 10,000 kmol/h. The second flash column operates with = 0.7, and the liquid product composition is 25 mol % MeOH. Determine the fraction vaporized in the first column, and the values yl, y2, x1, II, and I2. Feed = 10,000 kmol/h Z = 0.55 Column 1 Column 2 L2, X₂ = 0.25/nGiven the vapor-liquid equilibrium data in the table below, Methanol vapor (mol%) 0 13.4 23 30.4 36.5 Methanol liquid (mol%) 0 2 4 6 8 10 15 20 30 40 50 60 70 80 90 95 100 41.8 51.7 57.9 66.5 72.9 77.9 82.5 87 91.5 95.8 97.9 100 Temperature (°C) 100 96.4 93.5 91.2 89.3 87.7 84.4 81.7 78 75.3 73.1 71.2 69.3 67.6 66 65 64.5 Answer the following: Two flash distillation columns are connected together as shown in the following diagram. Both are at 1 atm. The feed to the first drum is a binary mixture of methanol and water of 55 mol % MeOH. Feed flow rate is 10,000 kmol/h. The second flash column operates with = 0.7, and the liquid product composition is 25 mol % MeOH. Determine the fraction vaporized in the first column, and the values yl, y2, x1, T1, and T2.See Answer
Q20:Q3) Equilibrium Flash Calculations A liquid containing 60 mol % toluene and 40 mol% benzene is continuously distilled in a single equilibrium stage at 1 atm. What percent of benzene in the feed leaves as vapor if 90% of the toluene entering in the feed leaves as liquid? Assume a relative volatility of 2.3.See Answer

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