ER100/PP184/ER200/PP284, Fall 2022󳆫Problem Set #2Total Points: 100 for ER110/PP184; 125 for ER200/PP284Show your work for complete credit. Online submissions must be a single PDF document, otherwisepoints will be deducted.1) “Soft” and “Hard” Energy Paths: Forty years ago Amory Lovins wrote his seminal piecedescribing “hard” and “soft” energy paths. In this question, we would like you to consider Lovins’sarguments in the context of important energy issues today, as well as compare the Lovins paper withsome of the articles you’ve read concerning energy and development. [25 points]a) Describe Lovins’s distinction between hard and soft paths in a few sentences using your ownlanguage. [5 points]b) Hard and soft are relative terms, and the same energy technology can be applied in ways that areconsistent with either the hard or soft approach. Pick an energy issue or technology and discusshow it might be viewed through a hard and soft energy path. [5 points]c) The Lovins piece is focused on energy in the context of the United States. What path do you thinkwould be best suited for developing countries (as in, those countries with average annual percapita energy consumption rates under 1 TOE) and why is this the same or different for developedcountries? [10 points]d) List the five fallacies in the “Mundane Science” article by Kammen and Dove, and discuss anyconnection between the points raised by Lovins and the five fallacies. [5 points]2) Combustion [23 points + 2 points for significant figures]: According to the BP Statistical Reviewof World Energy, fossil fuels (coal, oil, and natural gas) are the dominant (about 84.7%) energysources for the world’s 13.9 btoe (billion tons of oil equivalent) primary energy consumption in 2016.Similarly, in the United States, 84.3% of the 2.30 btoe primary consumption is from fossil fuels. Inthis problem we will examine the energy and carbon emissions from generating electricity using thesefuels. Assume energy density for coal and natural gas to be 29.8 MJ/kg and 50.7 MJ/kg respectively(i.e., that is the amount of thermal energy those fuels contain).a) Based on an approximate formula for coal (C10H8O1), and an approximate formula for natural gas(CH4), write the balanced combustion equation for each fuel. Assume complete combustion inoxygen. What are the CO2emission factors for coal and natural gas in kg/GJ? [8 points]b) Assume the efficiency of a new coal power plant is 35% and that of a natural gas combined cycleplant is 50%. What is the mass of carbon dioxide released per kWh of electricity generated fromeach plant? In the context of climate change, which one is a cleaner fuel and what attributes of thefuel make it so? [5 points]c) Suppose a student living in the United States (where the US average electricity generation fuelmix is 22% coal, 38% natural gas, and the remainder from non-carbon sources) consumes thenational average of 10,715 kWh of electricity per year, what are the annual CO2emissions (metrictons) attributed to that person’s consumption? Then assume this student moves to Berkeley, CA,where the fuel mix is 44% natural gas, no coal, and the remainder from non-carbon sources. If thestudent’s electricity consumption remains the same after moving to Berkeley, what are her annualCO2emissions (metric tons) now? For both calculations, assume the same power plant efficiencyas in part b) and transmission and distribution (T&D) loss of 10.% [3 points]d) The United States generated 1,733 TWh of electricity from coal in 2011, and 774 TWh ofelectricity from coal in 2020 (Source: EIA Electric Power Monthly, Table 1.1). Assume that theaverage efficiency of coal-fired power plants in the US is constant at 40%. How much less coal(in kilograms) did the US use to generate electricity in 2020 than 2011? If we piled this coal in anarea equal to the footprint of UC Berkeley’s campus (1,232 acres), what would be the height (ft)of this pile? Assume a simple rectangle, and the density of coal is 800kg/m3. [5 points]e) The total nameplate capacity of all coal-fired power plants in the United States is 234 GW as of2020. What is the average capacity factor of coal power plants in 2020? [2 points]3) Thermodynamics of Energy Systems [23 points + 2 points for significant figures]: Dynegy’sMoss Landing Power Plant in Monterey, a natural gas fired plant, used to be the largest generationfacility in the state of California with a total installed capacity of over 2,000 MW. The two newergenerators are still in operation, but two older generators were retired in December 2016. The twonewer generators (1,060 MW total) are combined cycle (using both the Brayton cycle for gas andRankine cycle for steam), and the older two generators (1,500 MW total) used gas turbines only (theBrayton cycle). Combined cycles are another way to improve the overall efficiency of a power plant.Assume the rate of energy added during the combustion of fuel when the generator is running at fullcapacity (not taking into account cycle efficiency) is 7,500 million Btu/hr for each old generator.Combined cycle natural gas power plants in California have an average annual capacity factor ofabout 45.7%.a) Draw 2 schematics showing the difference between the Brayton Cycle and Combined Cycle andlabel all components. In thermodynamic terms, briefly explain the function of each component,including what takes place in each component in terms of heat exchange, work, temperature andpressure. [13 points]b) Calculate the Carnot efficiency of a Brayton cycle system operating at the followingtemperatures. In one sentence, explain what Carnot efficiency represents. (Note: all temperaturesgiven in degrees Celsius) [3 points]:T1 = temps at exit of the exhaust heat exchanger and inlet of the compressor = 35.ºCT2 = temp at exit of the compressor and inlet of the combustor = 415ºCT3 = temp at the exit of the combustor and the inlet of the turbine = 990.ºCT4 = temp at the exit of the turbine and the inlet of the exhaust heat exchanger = 558ºCc) Calculate the 1st law efficiency of the generators that use the Brayton cycle. In one sentence,explain what first law efficiency represents. [2 points]d) What is the second law efficiency of the generator that uses the Brayton cycle? In one sentence,explain what second law efficiency represents. [2 points]e) As of 2020, what is the total energy output from the Moss Landing Power Plant in a typical year(in kWh) if the efficiency of a