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Questions and Answers

What is the overall purpose of the methane emissions studies discussed in the text?

The overall purpose of the methane emissions studies discussed in the text is to optimize feed intake in cattle to reduce methane emissions.

What type of facility are the cattle housed in?

The cattle are housed in naturally ventilated buildings.

From the graph, what is the value of the amplitude (A) of the periodic function?

  • 13.5 g/hr
  • 7 hours
  • 24 hours
  • 2.5 g/hr (correct)

    • The formula for the model of methane emissions is M = ______ * sin[(t − S)/24] + 13.5

    <p>2.5</p> Signup and view all the answers

    What are the units of the methane emission model M?

    <p>g/hr</p> Signup and view all the answers

    The graph in Question 1 represents the mean hourly methane emissions. Which of these is a possible limitation of this model?

    <p>All of the above. (D)</p> Signup and view all the answers

    Identify two general approaches for developing a suitable model for the data in Figure 2. Choose the two most suitable approaches from the following:

    <p>Functional form: Exponential, Power function (A), Develop a model: Use several points to determine constants, Use log-log and log-lin plots (C)</p> Signup and view all the answers

    In Question 2, what is the purpose of the DNN plume test?

    <p>The DNN plume test is designed to identify plumes of methane in the atmosphere.</p> Signup and view all the answers

    What is the prevalence (total number of plumes) in this sample?

    <p>5,660 (B)</p> Signup and view all the answers

    What is the probability of finding a plume if the DNN test predicts no plume?

    <p>9.4%</p> Signup and view all the answers

    Which of these is a disadvantage of the DNN plume test?

    <p>It misses more plumes than the SWIR bands plume test. (B)</p> Signup and view all the answers

    What is the annual rate of methane production by the landfill site in Mexico City after 11 years?

    <p>2 x 10⁷ m³/yr</p> Signup and view all the answers

    What quantity does the area under the curve represent in the context of methane production in a landfill?

    <p>The total methane produced over a given time period.</p> Signup and view all the answers

    Which of these methods can be used to estimate the accuracy of the trapezoid rule calculation?

    <p>All of the above (D)</p> Signup and view all the answers

    What is the methane production rate at the landfill site in Mexico City after 20 years?

    <p>0.8 x 10⁷ m³/yr</p> Signup and view all the answers

    What is the initial estimate (t0) used for the methane production model in Question 4?

    <p>5 years (B)</p> Signup and view all the answers

    What is the value of the methane production M(t) after 5 years?

    <p>1.372 x 10⁹ m³/yr</p> Signup and view all the answers

    What is the derivative of the methane production model M(t)?

    <p>M'(t) = (617.4 x 10³ – 68.6 x 10³t) t³.⁵e⁻⁰.⁵t</p> Signup and view all the answers

    What is the value of t1 after one iteration of Newton's method?

    <p>5.68 years</p> Signup and view all the answers

    What is the code snippet in the program for implementing Newton's method?

    <p>val = val - f(val)/df(val)</p> Signup and view all the answers

    What is the purpose of the condition 'abs(f(val)) > 0.0001' in the program?

    <p>The condition 'abs(f(val)) &gt; 0.0001' controls the iterations in the program. It ensures that the loop continues until the absolute value of the function f(val) becomes less than 0.0001, which is a criterion for stopping the iterations.</p> Signup and view all the answers

    What is the surge function that models methane production in an Australian landfill?

    <p>MAustralia(t) = 894.4 x 10³t⁴.⁸e⁻⁰.⁸t</p> Signup and view all the answers

    Which of these statements about the graphs of the two methane production models (Mexico and Australia) is true?

    <p>The Australian model reaches its maximum value at a higher time than the Mexican model. (C)</p> Signup and view all the answers

    What is the time it takes for the Australian landfill methane model to reach its maximum value?

    <p>6 years</p> Signup and view all the answers

    What is the time it takes for the Mexican landfill methane model to reach its maximum value?

    <p>9 years</p> Signup and view all the answers

    What is the general form of the rate of change equation for the methane production models discussed in the text?

    <p>M'(t) = r(1 − M / K) * M</p> Signup and view all the answers

    What value of K for the CD + WR model is provided in the text's context?

    <p>K = 83 mL/g</p> Signup and view all the answers

    Explain the physical significance of K in the context of methane production.

    <p>K represents the carrying capacity of the reactor. It signifies the total amount of methane that can be produced from the reactor given the input materials, after all reactions are complete. This represents the maximum value that the cumulative methane output can reach for a given amount of input.</p> Signup and view all the answers

    What is the value of the methane production (M) after one day using Euler's method for the CD + WR + CS model, using the parameters provided?

    <p>2.20 mL/g</p> Signup and view all the answers

    In the context of methane production models, why are they called models?

    <p>Methane production models are simplified representations of complex processes. They make assumptions and idealizations to capture and predict the behavior of the methane production system within the reactor. This simplification is done to make the system more manageable for analysis and prediction.</p> Signup and view all the answers

    Explain why the models can be useful for comparing methane production across different reactors, even if they are idealized.

    <p>Despite their idealities, the models can provide insights into the general trend of methane production under different conditions. These models allow for a comparative analysis across different scenarios, like comparing methane production in a reactor with CD + WR input to one with CD + WR + CS input. This allows researchers to evaluate the effects of different inputs and conditions on the overall methane production process while acknowledging the inherent limitations of the models.</p> Signup and view all the answers

    What is the primary source of methane produced by cattle?

    <p>Feed fermentation (D)</p> Signup and view all the answers

    Methane is a less potent greenhouse gas than carbon dioxide.

    <p>False (B)</p> Signup and view all the answers

    Which of these methods can be used to identify sources of methane emissions from space?

    <p>All of the above (D)</p> Signup and view all the answers

    What is the process by which organic matter is broken down in the absence of oxygen to produce methane?

    <p>Anaerobic digestion</p> Signup and view all the answers

    Study Notes

    Examination Information

    • Duration: 120 minutes
    • Planning time: 10 minutes
    • Permitted materials: Specified written/printed material, Casio FX82 or UQ-approved calculator
    • Materials provided: Additional exam materials (e.g., answer booklets, rough paper) may be provided upon request
    • Instructions: If a student believes there is missing/incorrect information, they should state this in their answer
    • Questions: Complete all questions in the space provided
    • Formula sheet: Detach the formula sheet from the back of the exam paper

    Rubric

    • Methodology (M): A valid approach is selected and makes progress towards addressing the requirements of the question.
    • Accuracy (A): The response adequately and accurately addresses the requirements of the question.
    • Communication (C): The key argument is expressed clearly and appropriately for the intended audience. Units and mathematical terminology are rigorous and graphs/diagrams are clear.
    • Reasoning (R): A reasoned argument is presented based on sensible logical deductions.

    Question 1

    • Methane Emissions Model: A study models methane emissions from cattle buildings across the day. The results are shown in a figure
    • Model development: A periodic function model is estimated for the methane emissions.

    Question 2

    • DNN Plume Test: One group developed a DNN Plume test to identify plumes of methane in the atmosphere.
    • Binary classification table: A table is created with 10,000 events to present the findings of the DNN plume test.
    • Probability of no plume: Given a negative result from the DNN plume test, the probability of no plume in that location is calculated via a percentage.
    • Comparison of models: The DNN test and SWIR bands plume test are compared. Arguments are made on which test is better in a given scientific context.

    Question 3

    • Landfill Methane Production: Data (Table 1) shows methane production at a Mexico City landfill site over time.
    • Graph: The provided graph is a visual representation of the methane production over time data in table 1.

    Question 4

    • Surge Function: Methane production is modeled as a surge function.
    • Newton's Method: The method is used to approximate the time 't' at which methane production first reaches 2x10^7 m³/yr.
    • Calculating parameters: The equations for the function and its derivative are provided to assist with the process

    Question 5

    • Anaerobic Digestion Models: Models are being built to explain the amount of methane produced in anaerobic digestion reactors, comparing different organic inputs.
    • Differential Models: The rate of change of the cumulative methane output is modeled using a function with constants.
    • Value of K: The value of 'K' for a specific model is estimated and explained its significance physically.
    • Euler's method: Used to estimate the methane value for the model 'after 1 day'.

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