SCIE1000 Semester 2 2024 Theory & Practice in Science Past Paper PDF

Semester Two Examinations, 2024 SCIE1000 Venue ____________________ Seat Number __________...

Semester Two Examinations, 2024 SCIE1000 Venue ____________________ Seat Number __________ Student Number |__|__|__|__|__|__|__|__| Family Name ____________________ This exam paper must not be removed from the venue First Name ____________________ School of Mathematics & Physics Semester Two Examinations, 2024 SCIE1000 Theory & Practice in Science This paper is for St Lucia Campus students. Examination Duration: 120 minutes For Examiner Use Only Planning Time: 10 minutes Question Mark Exam Conditions: 1a 1b Specified written or printed material permitted Casio FX82 series or UQ approved and labelled calculator only 1c During Planning Time - Students are encouraged to review and plan responses to the exam questions 2a Materials Permitted in the Exam Venue: (No electronic aids are permitted e.g. laptops, phones) 2b One A4 sheet of handwritten notes double sided is permitted 2c Materials to be supplied to Students: Additional exam materials (e.g. answer booklets, rough paper) will 3a be provided upon request. 3b None 3c Instructions to Students: If you believe there is missing or incorrect information impacting your ability to answer any question, please state this when writing 4a your answer. 4b Complete all questions in the space provided. 4c You may detach the formula sheet from the back of the exam paper. 5a 5b 5c Total _________ Page 1 of 18 Semester Two Examinations, 2024 SCIE1000 Rubric This exam requires students to demonstrate the ability to: ˆ Select and implement an appropriate solution methodology. ˆ Accurately calculate quantities, evaluate information, and/or convey scientific/mathematical/ philosophical/programmatic concepts. ˆ Communicate key ideas clearly, concisely, and precisely, showing a consideration for the audience of their work through an appropriate choice of communication style and terminology. ˆ Articulately synthesise information to provide a reasoned argument that is supported by appro- priate evidence or justification. The following provides a guide as to the achievement standard expected for each of these assessment criteria. Appropriate working should be shown in all cases, where relevant. Methodology (M) Score M1 A valid approach is selected that makes progress towards addressing the requirements of the question. Note: the accuracy of the results should be assessed separately. M0 Does not meet the criteria for a 1. Accuracy (A) Score A1 The response adequately and accurately addresses the requirements of the question. A0 Does not meet the criteria for a 1. Communication (C) Score C1 The expression of the key argument is clear, and the language and approach used are appropriate for the intended audience. Units are presented where appropriate. The use of any mathematical terminology and notation is rigorous. Any graphs or diagrams are clear, appropriately detailed, and adequately labelled. Does not mislead. C0 Does not meet the criteria for a 1. Reasoning (R) Score R1 A reasoned argument is presented based on the synthesis of sensible logical deductions consistent with the information provided. R0 Does not meet the criteria for a 1. These criteria may be represented in any combination. More than one mark may be assigned to a single criterion for a given question where the indicated skill is required to be demonstrated more than once. Page 2 of 18 Semester Two Examinations, 2024 SCIE1000 Attempt all questions. To answer each question you may need to use methane emissions information that is provided on page 17. Question 1 A study has been conducted to improve understanding of the fluctuations in methane emissions in cattle farming across the day. The overall purpose of these types of studies is to optimise feed intake (the type of food and when it is consumed) to reduce the methane emissions of cattle. This study was carried out over two seasons at two farms with cattle being held in naturally ventilated buildings. The mean hourly methane emissions (across the two seasons) are shown in Figure 1. 16 Methane emissions per animal (g/hr) 15 14 13 12 11 0 5 10 15 20 Time of day (hours) Figure 1: Mean hourly methane emissions from cattle buildings (a) Develop an approximate model of the methane emissions, M , as a function of time, t, using the periodic function introduced in this course. Ensure you quote values for each constant in your model. (3 marks, A2 C1) (question continued over) Page 3 of 18 Semester Two Examinations, 2024 SCIE1000 (b) Write a paragraph explaining two potential limitations of your model. Your audience is a first-year university student studying science. (2 marks, C1 R1) (question continued over) Page 4 of 18 Semester Two Examinations, 2024 SCIE1000 (c) (Advanced) The researchers also explored the role that temperature plays in modelling hourly emissions. Figure 2 illustrates the relationship between methane emissions and temperature, taken at 1am daily on 60 days throughout the period of this study. 35 Methane emissions per animal (g/hr) 30 25 20 15 10 5 10 0 10 20 Temperature at 1am ( ) Figure 2: Methane emissions from cattle buildings at 1am Without performing any calculations, explain how you would approach developing a suitable model for the data in Figure 2. (2 marks, M1 R1) Page 5 of 18 Semester Two Examinations, 2024 SCIE1000 Question 2 Locating sources of anthropogenic methane emissions is an important and challenging undertaking. If it is possible to accurately locate plumes of methane entering the atmosphere using satellite imagery, this could lead to identification of otherwise unknown sources of methane emissions, and strategies could then be used to reduce these emissions. One group of researchers has developed a test, which we will denote the DNN plume test, to identify plumes of methane. (a) Create a binary classification table for the DNN plume test using a sample size of 10 000 events. Ensure that you explain the steps you take to develop the table. (3 marks, M1 A2) (question continued over) Page 6 of 18 Semester Two Examinations, 2024 SCIE1000 (b) The DNN test predicts no plume in a given location. What is the probability that there is no plume in that location? (2 marks, M1 A1) (c) (Advanced) We wish to compare the DNN test to the SWIR bands plume test. Which do you think is a better test in this scientific context? Explain your reasoning. (2 marks, R2) Page 7 of 18 Semester Two Examinations, 2024 SCIE1000 Question 3 Data on the annual rate of methane produced by a landfill site in Mexico city is presented in Table 1. Time t (year) 0 3 7 9 11 20 Methane production M (m3 /yr) 0 1.3 × 107 2.5 × 107 3.0 × 107 2 × 107 0.8 × 107 Table 1: Methane production at a Mexico City landfill site (a) Use the axes below to plot the data provided, with time on the horizontal axis and methane production on the vertical axis. Join the data points with straight lines. Ensure that your graph is appropriately communicated. (2 marks, A1 C1) (question continued over) Page 8 of 18 Semester Two Examinations, 2024 SCIE1000 (b) Apply the trapezoid rule to calculate the total methane produced over the 20 year period (area under the curve). (3 marks, M1 A2) (c) (Advanced) It is an important scientific skill to be able to estimate the accuracy of any particular calculation. Describe one way this could be achieved for the area under the curve calculation in part (b). Your audience is a SCIE1000 student just starting the course. Ensure you include the estimate that is calculated using your method. (2 marks M1 C1) Page 9 of 18 Semester Two Examinations, 2024 SCIE1000 Question 4 The methane produced by the Mexico City landfill site can be modelled by a surge function of the form M (t) = 137.2 × 103 t4.5 e−0.5t where M is in the units of m3 /yr and t is in units of years. (a) Given a starting estimate of t0 = 5 years, use a single iteration of Newton’s method to approximate the value of t where the methane production of the landfill site in Mexico City, M (t), first reaches 2 × 107 m3 /yr. Note that M ′ (t) = 617.4 × 103 − 68.6 × 103 t t3.5 e−0.5t
(3 marks, M1 A1 C1) (question continued over) Page 10 of 18 Semester Two Examinations, 2024 SCIE1000 (b) The program below implements Newton’s method. import numpy as np # Define the function and its derivative def f(t): return 137200 * pow(t, 4.5) * np.exp(-0.5 * t) - 20000000 def df(t): return (617400 - 68600 * t) * pow(t, 3.5) * np.exp(-0.5 * t) # Insert comment 1 here val = float(input("What is the initial estimate?")) # Insert comment 2 here i = 0 while(abs(f(val)) > 0.0001): val = val - f(val)/df(val) i = i+1 print("Step ", i, ":", round(val,3)) # Output print("Estimated time is: ", round(val,3), "years" ) (i) Provide informative comments to replace insert comment X here for the 2 comments in the code. (1 mark, C1) (ii) Explain the role of abs(f(val)) > 0.0001 in the program. (1 mark, R1) (question continued over) Page 11 of 18 Semester Two Examinations, 2024 SCIE1000 (c) (Advanced) A hypothetical landfill facility in Australia sorts rubbish into different components before being sent to landfill. A surge function for the organic landfill is given by MAustralia (t) = 894.4 × 103 t4.8 e−0.8t Without plotting M (t) and MAustralia (t), briefly discuss how their graphs would appear against time, including any similarities and differences. (2 marks, M1 R1) Page 12 of 18 Semester Two Examinations, 2024 SCIE1000 Question 5 In , the authors are interested in building models to explain the amount of methane being produced by an anaerobic digestion reactor, by comparing different sources of organic input matter. The first model uses a combination of cow dung (CD) and wine residue (WR) as inputs, while the second model also includes corn straw (CS) as an input. The cumulative methane output from the reactor, M , is measured over time, t, as mL/g of organic input matter from the various sources. Plots are shown in Figure 3. The researchers determined that the rate of change for the two models of cumulative methane outputs, M ′ , will have the form:   ′ M M (t) = r 1 − M K where r and K are constants. 80 CD + WR Cumulative methane output (mL/g) CD + WR + CS 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 Digestion time (days) Figure 3: Anaerobic Digestion (a) Estimate the value of K for the CD + WR model and explain its physical significance in this context. (2 marks, A1 R1) (question continued over) Page 13 of 18 Semester Two Examinations, 2024 SCIE1000 (b) Find the value of M for the CD + WR + CS model after 1 day using Euler’s method to solve the differential equation using the following parameters: r = 0.14 day−1 , K = 69.1 mL/g and M (0) = 1.93 mL/g, using a time step of 0.5 days. (3 marks, M1 A2) (question continued over) Page 14 of 18 Semester Two Examinations, 2024 SCIE1000 (c) (Advanced) Using what you have learned in the philosophy of science component of SCIE1000: (i) Explain why the models of methane production are models. In doing so, state some of the ways in which the models might be idealised. (1 mark, R1) (ii) Explain why, despite their idealised nature, the models may be useful in comparing the methane production of a reactor with a CD + WR input and another reactor with a CD + WR + CS input. (1 mark, R1) Page 15 of 18 Semester Two Examinations, 2024 SCIE1000 Extra space for working This space can be used if you need extra space to answer any of the questions. Clearly indicate the question(s) that you are answering. Ensure that you also put a note within the body of the relevant question(s) directing the marker here. References Hempel, S., Willink, D., Janke, D., Ammon, C., Amon, B. and Amon, T. (2020). Methane emission characteristics of naturally ventilated cattle buildings. Sustainability, 12(10), 4314. Joyce, P., Ruiz Villena, C., Huang, Y., Webb, A., Gloor, M., Wagner, F. H. and Boesch, H. (2023). Using a deep neural network to detect methane point sources and quantify emissions from PRISMA hyperspectral satellite images. Atmospheric Measurement Techniques, 16(10), 2627-2640. Meraz, R. L., Vidales, A. M. and Dominguez, A. (2004). A fractal-like kinetics equation to calculate landfill methane production. Fuel, 83(1), 73-80. Zhang, H., An, D., Cao, Y., Tian, Y., and He, J. (2021). Modeling the methane production kinetics of anaerobic co-digestion of agricultural wastes using sigmoidal functions. Energies, 14(2), 258. Stocker, T (2014). Cambridge university press. Climate change 2013: the physical science basis: Working Group I contribution to the Fifth assessment report of the Intergovernmental Panel on Climate Change Etminan, M., Myhre, G., Highwood, E. J. and Shine, K. P. (2016). Radioactive forcing of carbon dioxide, methane, and nitrous oxide. A significant revision of the methane radiative forcing. Geophysical Research Letters, 43(24), 12-614. Global Methane Initiative, United States Environmental Protection Agency. https://www.epa.gov/gmi/importance-methane. Accessed 26 August 2024 Livestock methane and nitrogen emissions, Agriculture Victoria. https://agriculture.vic.gov.au/climate-and-weather/understanding-carbon-and-emissions. Accessed 26 August 2024 O’Neill, K. (2022). Convolutional Neural Networks for Detection of Point Source Methane Plumes in Airborne Imaging Spectrometer Data (Master’s thesis, The University of Utah). How Does Anaerobic Digestion Work?,United States Environmental Protection Agency. https://www.epa.gov/agstar/how-does-anaerobic-digestion-work. Accessed 26 August 2024 (Information and formula sheets over) Page 16 of 18 Semester Two Examinations, 2024 SCIE1000 Information sheet: methane Background Methane (CH4 ) is a powerful greenhouse gas with a warming potential which, per unit mass emitted, is 84 times larger than for carbon dioxide over a 20-year period. Emissions of methane as a result of human activities (anthropogenic) have contributed to one-quarter of climate warming since pre- industrial times. Major anthropogenic sources of methane include landfill, oil and gas activities, coal mining and agricultural activities, including cattle farming. Because methane is both a powerful greenhouse gas and short-lived compared to carbon dioxide, achieving significant reductions would have a rapid and significant effect on atmospheric warming potential. Measuring methane in naturally ventilated cattle buildings Ruminant livestock, including cattle, have microbes in their rumen called methanogens. These mi- crobes produce methane (from the fermentation of feed) that is then belched out. Altering the type and timing of feed being given to the cattle can have an effect on overall methane emissions from this type of farm, where feed can be controlled. Testing for sources of methane emissions There is considerable interest in using satellite imagery to identify sources of methane emissions. Sometimes this method can detect otherwise unknown sources (such as undisclosed landfill sites, ex- cess methane escaping from underground coal mines or gas pipeline leaks). One test, called the DNN test, uses satellite images to identify plumes of methane entering the atmo- sphere. This test is shown to have a sensitivity of 92.3% and a specificity of 96.7% on sites known to have a prevalence of 56.6%. An alternative test, called the SWIR bands plume test, has a sensitivity of 20%, and a specificity of 100%. Methane produced by landfill sites Landfill is a significant contributor to global methane emissions. A group of researchers have under- taken a simulation study on a landfill site based in Mexico city. Waste was added to the site in initial years, after which the site was left to decompose. The annual rate of methane output from the site was estimated based upon the composition of the waste (some waste products - such as food waste - decompose and generate methane at a higher rate than others - such as textiles). Anaerobic digestion Anaerobic digestion is a process through which bacteria break down organic matter, producing a number of useful outputs, including methane (which is the main ingredient in natural gas). This takes place in a reactor so that the methane can be captured and used for a variety of applications. These reactors are used for industrial purposes to manage waste and to produce fuels. (Formula sheet over) Page 17 of 18 Semester Two Examinations, 2024 SCIE1000 Formula Sheet Multiple Prefix Symbol Multiple Prefix Symbol 101 deca da 10−1 deci d Base quantity SI unit name Symbol 102 hecto h 10−2 centi c length metre m 103 kilo k 10−3 milli m mass kilogram kg 106 mega M 10−6 micro µ time second s 109 giga G 10−9 nano n electric current ampere A 1012 tera T 10−12 pico p thermodynamic temperature kelvin K amount of substance mole mol 1015 peta P 10−15 femto f luminous intensity candela cd 1018 exa E 10−18 atto a 1021 zetta Z 10−21 zepto z 1024 yotta Y 10−24 yocto y Quantity Name Symbol SI units SI base units frequency hertz Hz - s−1 force newton N - m · kg · s−2 pressure, stress pascal Pa N · m−2 m−1 · kg · s−2 energy, work, quantity of heat joule J N·m m2 · kg · s−2 power, radiant flux watt W J · s−1 m2 · kg · s−3 electric potential difference, electromotive force volt V W · A−1 m2 · kg · s−3 · A−1 ◦ Celsius temperature degree Celsius C - K function type general form linear y = mx + c Newton’s method xi+1 = xi − ff0(x i) (xi ) quadratic y = ax2 + bx + c power y = axp Trapezoid rule Atrap = (x2 − x1 )( y1 +y 2 ) 2 periodic y= A sin( 2π P (t − S)) + E exponential y = Ce kt Euler’s method ti+1 = ti + h yi+1 = yi + hyi0 surge y = atp e−bt True Status Yes No Lotka-Volterra model Test Positive A B Q0 = aQ − bP Q Test Negative C D P 0 = −cP + dP Q N =A+B+C +D A+D SIR model accuracy = N S A S 0 = −a I sensitivity = N A+C S I0 = a I − bI D N specificity = 0 B+D R = bI Page 18 of 18