PHYS Midterm I

Transcription

1 PHYS Midterm I January 30, pts total Please attempt all questions and show your work in the exam booklet provided. Equations and other useful information can be found at the back of the exam. 1. (1 pt) The oil that we burn in our cars today represents solar energy that was captured in organic molecules approximately years ago: A) 200,000 B) 2,000,000 C) 20,000,000 D) 200,000,000 E) 2,000,000, (1 pt) The following province does not obtain a large proportion of its electricity from hydro A) British Columbia B) Ontario C) Quebec D) Manitoba E) none of the above 3. (4 pts) Classify the following terms according to whether they represent energy (E) or power (P) or neither (N): (a) calorie (b) joule-second (c) kilowatt-hour (d) tonnes of oil equivalent (e) electron volt (f) Bbl (g) kg m 2 /s 3 (h) horsepower 1

2 4. (4 pt) Coal resources in the US are currently estimated at EJ. At the current production rate, the lifetime is estimated to be 1500 yr. (a) Compare the approximate lifetime of this resource given steady growth in US coal production at i. 1.0% per year ii. 2.0% per year iii. 5.0% per year (b) What is the doubling time of the rate of production at 5.0% growth per year? 5. (5 pts) When a lead bullet smashes into a wall, all of its kinetic energy is converted into thermal energy. Estimate the minimum speed that the bullet must have in order to melt on impact. Assume that the mass of the bullet is 125 g. 6. (10 pts) Oil production has grown dramatically in Brazil. In 2007, A. Szklo et al published an article that used the Hubbert model to provide insight into future development. Their figure, reproduced below, shows three curves based on estimates of the total recoverable resource, Q. The production, in units of millions of barrels of oil per day, is plotted over a period of 140 years ARTICLE IN PRESS A. Szklo et al. / Energy Policy 35 (2007) Mbpd P50 Cumulative Production P30 P75 Fig. 1. Hubbert curve for Brazilian oil production with different probabilities. Note: the P75 estimate is detailed in Szklo et al. (2005). According to the accumulated discovery data, Brazil s proven and potential reserves and the log-normal curves adjustment, for P75, EUR was estimated at billion barrels. For P50, EUR was estimated at billion barrels and for P30, EUR reached billion barrels. For the middle estimate, shown with a dash-dot-dot curve, and the data shown for 2004, estimate the total recoverable resource used for the model function. Express evolution of Brazil s oil reserve estimates drawn up by the USGS, for a period of less than 10 years. For the 1988 base year, the USGS forecast Brazil s EUR at around 10 billion barrels, yourwith answer a 50% inprobability. terms offor barrels the 1993 ofbase oil. year, this forecast rose to almost 30 billion barrels. 20 Finally it reached an estimate of around 60 billion barrels, which was the one applied in this paper, considering the USGS data for the 1996 base year (USGS, 2000). It seems that, for non-mature areas, such as Brazil, probability of adding 2 reserves means also degree of knowledge. Therefore, it is more a Bayesian probability, than a classical probability. 21 production areas, where the number of exploratory wells per square kilometers is high. An important reclassification of Brazilian reserves should be expected, as exploratory efforts are stepped up in the country. Thus, using a Bayesian probability concept, Brazil s P30 reserves might be dynamically more likely than the P30 reserves in mature basins in other producing areas elsewhere in the world. Indeed, it is more likely that the certainty associated to part of Brazil s P30 reserves will rise over time, in parallel to the increase in associated knowledge (or the increase of the exploratory efforts). This is a characteristic of frontier areas such as Brazil. This also

3 7. (10 pts) An electric power plant can deliver 1000 MWe of power continuously. (a) Assuming the overall efficiency of the plant is 33%, how many tonnes of coal must be put into the boilers every 24 hours? (b) How many tonnes of CO 2 are released by the power plant into the atmosphere every 24 hours? Use the approximation that the coal is 100% carbon. One mole of oxygen has a mass of 16 g. (c) How many Btus of thermal energy must be extracted by the heat exchanger and dissipated every 24 hours? 3

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5 Equations and other useful information: C.O.P. Refrigerator C.O.P. Heat P ump N = N o exp(k t) k = ln(1 + λ) T = 1 ( ) k k ln QT + 1 N o [ ] z 2 N = N M exp 2 Q = σ 2π N M z = t T M σ Q = m c T Q = m L F Q = m L v η T 1 T o T 1 T o T 1 T o T 1 T 1 T o Average radius of the Earth m Energy content of coal J/kg Energy content of crude oil J/kg specific heat for lead J kg 1 K melting temperature for lead 327 C latent heat of fusion for lead J/kg latent head of vaporization for lead J/kg specific heat of water J kg 1 K specific heat of ice J kg 1 K latent heat of fusion of water J/kg density of water 1000 kg/m 3 1 Btu 1055 J 1 tonne of crude oil 7.3 barrels Symbol Prefix Factor T tera E exa

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