ER100/PP184/ER200/PP284, Fall 2022 Problem Set #7 Total Points: 100 for ER110/PP184; 125 for ER200/PP284 1) Competing Uses of Biomass [25 points] Biomass can be used to create ethanol fuel. It can also be used to generate electricity, that can then be used to charge electric vehicles (EVs). In this problem, you will determine whether ethanol or electricity can provide a higher biomass‐to‐wheel efficiency. Assume that one hectare of cropland can produce 14 tons of dry switchgrass per year and that dry switchgrass has an energy density of 15 MJ/kg. a) Each ton of dry switchgrass can be processed to produce 73 gallons of ethanol. Ethanol has an energy density of 92 MJ/gallon. Assume that the internal combustion engine (ICE) is 23% efficient in converting fuel energy to useful work at the wheels (motion). With what efficiency is biomass energy delivered to the wheels in this ICE car? (5 points) b) Alternatively, each ton of dry switchgrass could be used directly to generate electricity, and this electricity could in turn be used to operate an EV. Assume that a biomass‐fueled power plant has a first-law efficiency of 37%. There is a 8.0% loss for transmission and distribution of electricity from the power plant to the car charging station. The motor plus battery is 85% efficient in converting electrical energy delivered from the charging station to mechanical work. With what efficiency is biomass energy delivered to the wheels in this EVICE car? (5 points) c) According to the above analysis regarding these two uses of biomass for transportation, if we are concerned about utilizing biomass resources most energy efficiently, should we use biomass to generate electricity or should we use it to produce liquid fuels? Many factors are left out in this analysis. Using what you’re learned throughout this class, mention and briefly explain two shortcomings of this simplified analysis. (10 points)d) Let’s assume switchgrass is used to produce ethanol for use in 100% ethanol‐fueled vehicles. How much land (in km2) would be required for switchgrass production to provide enough ethanol to meet the fuel demand of all cars in the United States? (Assume 264 million cars traveling an average of 13,000 mi/yr with an average fuel economy of 24 miles/gallon ethanol.) Roughly which US state is this land area comparable to? (https://en.wikipedia.org/wiki/List_of_U.S._states_and_territories_by_area) (5 points) 2) Lithium Batteries [ER200/PP284 ONLY 25 points]: a) Let’s assume that a first-generation Tesla Powerwall is made up of battery cells that use graphite (C6) in the anode and lithium cobalt oxide (LiCoO2) in the cathode. Assume each cell’s capacity is 2.7 Ah and has a voltage of 4.4 V. If the Powerwall’s total storage capacity is 7.00 kWh, how many cells are there? What is the total mass of anode (kg) and cathode (kg) material in the Powerwall? Assume that the energy content of 1 gram of graphite is 370 mAh/g, and the energy content of 1 gram of LiCoO2 is 137 mAh/g. You may find it useful to review the materials from Section 10 for this problem. [10 points] b) How many lithium ions are in the Powerwall? What is the mass (in grams) of lithium per Powerwall? Assume 1.0 lithium ion per unit charge (100% of lithium atoms go through the oxidation reduction reaction) and the molar mass of lithium is 6.94 g/mol. One unit charge (q) is 1.6x10-19 coulombs, and one coulomb is one Ampere-second. [5 points] c) Total lithium deposits in the world are estimated at 20 x 109 kg. One concern about Li-ion battery technology is the diminishing and finite amount of the lithium resource; it is estimated that all the lithium in the world could only electrify 62% of the world’s vehicle fleet. If 500 million homes were to install a first-generation Powerwall, what percentage of the world’s lithium resources would be used up? [5 points] !d) Review the following discharge curves for a lithium coin battery (the type commonly found in watches). The battery has a rated capacity of 240 mAh and a voltage cutoff of1.6 V, below which the voltage is too low to power the device. Estimate the difference in energy delivered when the rate of discharge is 3.0 mA vs. 0.5 mA. Your estimates can be very rough – one significant figure – so long as they are grounded in the basic characteristics of the discharge curves. What explains the difference? [5 points] 3) Net Zero America [50 points] The Net Zero America project, developed by a group of researchers at Princeton University, lays out five potential pathways to decarbonizing the U.S. economy by 2050. Modeling methodology and results can be found at https://netzeroamerica.princeton.edu. Use this site to answer the following questions. a) In a few sentences, explain why we discuss climate change in a course like Energy and Society. What is the relationship between energy and climate change? What is the relationship between climate change and society? [5 points] b) List the five pathways for decarbonization. What are the major similarities and differences between these pathways? Include at least three similarities and three differences. [5 points] c) List the six pillars of decarbonization. [5 points]For the following parts, use data from the reference scenario in 2050 and the highly electrified demand/100% renewable supply scenario in 2050. i) Efficiency: What is the percent change in final energy use and total emissions between the reference and decarbonized scenarios? Qualitatively, how might these values change in an optimal scenario with fewer constraints? [5 points] ii) Electrification: What fraction of total energy use is met by electricity in the reference and decarbonized scenarios? Break this down by end use sector (transportation, residential buildings, commercial buildings, and industry) for each scenario. List the sectors in order of smallest to largest change in electrification. Qualitatively, how might these values change in an optimal scenario with fewer constraints? [5 points] iii) Clean Electricity: For both the reference and decarbonized scenario, what percent of total electricity generation comes from renewable sources (solar, wind, hydro, geothermal, biomass)? What about zero emission sources (including nuclear and fossil with carbon capture)? Qualitatively, how might these values change in an optimal scenario with fewer constraints? [5 points] iv) Clean Fuel: What is the percent change in