Homework # 1 Total points: 85 Module 3: Energy, Sustainability and Resource Estimation Sustainable Energy System Engineering Name (Print): (First, Last) ID: Date of submission: Homework Submission Rules: (1) (2) (3) (4) Print this question paper and write your answer on it Work to solve the problem must be shown (i.e. Hand Written solution). Problem solutions must be in numerical order. The staple which holds the project/homework together must not prevent reading the problem number and problem solution. (5) Put a box around answers, if applicable. (6) The solution pages within a problem should be in the correct order. (7) Each problem must be correctly numbered. (8) The complete page of the MATLAB printouts must be submitted, if applicable. (9) Copying of project/homework is not permitted. (10) Points are deducted if the rules are not followed. Problems: 1. Coal fired power plants close to Kansas City are located in Sibley and Iatan. These power plants are super critical units i.e. they operates at supercritical state hence they are highly efficient. (Critical temperature and pressure for water is 374 0C and 22 MPa approx. respectively) Typical coal consumption rate of this type of power plant is 2746 Metric Tons per MW per Annum. Iatan has two units, Unit 1 with capacity 651 MW and Unit 2 with capacity 850 MW. Sibley power plant has three units, combined capacity of which is 524 MW. Average life time of coal fired power plant is 40 years. Calculate the total impact of coal of these power plant during their life time. Carbon content of this coal is typically 75-78%. Complete combustion of 1 short ton (2,000 pounds) of this coal will generate about 5,720 pounds (2.86 short tons) of carbon dioxide. Based on this information calculate how much CO2 these plants will release to the atmosphere. (Points 10+10 = 20) Soln. 2. The exponential growth model N = 30 e0.0198026t describes the population of a city in the United States, in thousands, t years after 1994. Use this model to solve the following questions: a. What was the population of the city in 1994? (Points 5) b. By what % is the population of the city increasing each year? (Points 5) c. What will the population of the city be in 2005? (Points 10) d. When will the city’s population be 60 thousand? (Points 10) Soln. 3. Even though government of many countries are in limbo what to do cryptocurrency but economists have admitted that they are assets and are not going to go away from financial market anytime soon. Suppose you bought ten bitcoins this year. Price of each of them is $15000.00. “Price increase” of these bitcoins follows an exponential growth model of P = P0*e^0.0645t, where P0 is the current price and t is the time in year. How many years you’ve to wait to sell these bitcoins to make a profit of $50000.00? (Points 15) Soln. 4. Saudi Arabia has oil reserve of 268 billion barrels at present. Current production rate is 10 million barrel per day. At this production rate, how long (year) this reserve will last? If they yearly production rate increases by 5%, how long this reserve will last? Use both ‘Resource life time’ equation, Exponential decay equation/mean life time equation to calculate it. Discuss the result. (Points 3+10+5+2=20) Soln. 5. As carbon-14 (C-14) is a radioactive material, hence it decays overtime through radiation. An artifact originally had 12 grams of carbon-14 present. The decay model A = A0 *e^(-0.000121t) describes the amount of carbon-14 present after t years. How many grams of carbon-14 will be present in this artifact after 10,000 years? (Points 10) Soln. 6. A certain radioactive isotope element decays exponentially according to the model A = A0 *e^(-0.25t), where A is the number of grams of the isotope at the end of t days and A0 is the number of grams present initially. What is the half-life of this isotope? (Points 10) Soln.
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