/ER100/PP184/ER200/PP284, Fall 2021Problem Set #1 Energy Units & Conversions, Global Energy UseTotal Points: 100 for ER110/PP184; 125 for ER200/PP284 Due September 10The purpose of these problems is to begin to get you comfortable with the wide array of energyunits used, and to gain experience in both doing calculations, and in finding other information you need by hunting around. Show your work for complete credit. Online submissions must be a single PDF document, otherwise points will be deducted.1. Warm up [25 points]a. One of the fundamental components of energy literacy is understanding the distinction between energy and power. In your own words, provide definitions for these two concepts. Use kilowatts and kilowatt-hours to discuss the relationship between energy and power. (5 points)Energy is the capacity of a physical system to perform work. Power is the rate of flow of energy over time. Thus, kilowatts (kW) is units of power and kilowatt-hours is units of energy. b. Assume that current global power usage rate is approximately 15TW. What percent is this of total solar radiation incident at the top of the earth’s atmosphere? What source provides the largest % of current human use? (5 points). Two different numbers are given in the Toolkit Appendix for incident solar radiation, so either answer is acceptable (other answers also acceptable if a different number is used and cited):15TW175,000TW=0.0086 % -or- 15TW162,000TW=0.0092%Oil is the largest source of energy services.c. Suppose a refrigerator operates with average power consumption of 65 We. How much energy in kWhe is consumed by the refrigerator per year? (5 points)65 Werefrigerator×24 hd×365 dyr=569.4 → 570 k Whe/ y (2 sig figs)d. Tour de France riders consume about 5,200 Calories per day of the race. Calculate a rider’s average power intake in Watts over the 21 days of the Tour. [Power intake is the rate at which the rider consumes energy in the form of food. The actual energy used to propel the rider’s bike, kinetic energy, is less than the energy they eat. There is some energy loss due to inefficiencies in converting between food and usable energy, maintaining body heat, etc. but we ignore this here.] (5 points)5200Cald∗1000 calCal∗1 J0.239 cal∗WsJ∗1h3600 s∗1d24 h=250 Watts (2 sig figs)Note: it is irrelevant that the Tour lasted for 21 days. All you need to know is the amount of energy the cyclist consumed per day, because (power = energy / time).e. The rated power of the GE’s largest wind turbine is an amazing 12.0 MW1. Assuming its average capacity factor* is 45%, how much energy does the wind turbine produce per year? If 100% of electricity demand of the City of Berkeley will come from these GE windturbines, how many wind turbines will be necessary? (Assume that an average citizen in Berkeley consumes 6.7 MWh/year.) (5 points) *In this class we define capacity factor as the ratio of actual energy output to possible energy output over a given time period. We will cover this concept in greater detail in Week 3 section.12.0 MWturbine×24 hd×365 dyr×0.45=47,304 → 4.7 × 103MWh/turbine / yr6.7 MWhyear person×121,363 people [1]Berkeley×turbine yr47,304 MWh=17.19→ 18 turbines/ BerkeleyWe round up from 17.19 to 18 here because of the phrasing of the question: the turbines need to supply 100% of electricity demand, and 17 turbines wouldn’t be sufficient to supply that demand.[1] Population of Berkeley in 2019: https://www.census.gov/quickfacts/berkeleycitycaliforniaA different answer may be acceptable if consistent with the number used for the population of Berkeley, and the source is cited.2. Electricity and unit conversion [25 points] In 2015, the total amount of electricity generation in California was 196 billion kWh. For the problems below, assume that 30% of the energy available in the following fuels can be converted to provide for this amount of electricity, unless otherwise indicated. (Later in the course, we’ll show you where this assumption comes from.) Please refer to “Toolkit Appendices” for various conversion rates.a. How many joules of energy is this equivalent to? Express your answer in TJ/year. (3 points) 1 https://www.popularmechanics.com/science/energy/a25956533/ge-largest-wind-turbine/196 billion kWh/y = 196x109 kWh/yr x 3.6 x 106J1 kWh x 1 TJ1012J = 705.6x103 TJ/yr ≈ 706x103 TJ/yrb. How many barrels of oil would be required to produce this much electricity? (2 points)196x109 kWhe x 1 kWhth0.3 kWhe x 3.6 x 106J1 kWhth x 1 bbl oil6.1 x 109 J = 40x107 bbl oil c. How many kilograms of nuclear fuel? (The fuel fed into a Pebble Bed Modular reactor contains 270,000 MWd [Megawatt-day] of energy per metric ton. The efficiency of such a reactor is 30%.) (3 points)196x109 kWh x 1kWd24 kWh x 1 MWde1000 kWd x 1 MWdth0.3 MWde x 1 t fuel2.7 x 105MWdth x 1000 kg1t = 1 x105 kg fueld. How many kilograms of wood? (2 points) 196x109 kWhe x1 kWhth0.30 kWhe x 3.6 x 106J1 kWhth x 1kg wood15 x 106J = 2 x 1011 kg woode. How many kilograms of coal? (2 points) 196x109 kWhe x 1 kWhth0.3 kWhe x 3.6 x 106J1 kWhth x 33 kg coal1.0 x 109 J = 8 x 1010 kg coal f. How many cubic feet of natural gas? (Note the temperature and pressure, if known.) (2 points) 196x109 kWhe x1 kWhth0.3 kWhe x 3.6 x 106J1 kWhthx 1m3natural gas3.9 x 107J x 35.3 ft31 m3 = 2 x1012 ft3 natural gasg. How many square meters of solar panels would be required to produce this much electricity? (assume that the panels are in an area with an annual average solar radiation of 5.7 kWh/m2/day, and that the solar panels have a conversion efficiency of 14%) (3 points)196x109 kWhe/yr x 1kWhincoming0.14 kWhe x 1 m2• day5.7 kWhincoming x 1 yr365 days = 6.7x108 m2 solar panelsh. How many gallons of water need to fall the height of Niagara Falls? Assume that 1 kg of water at a height of 1 meter stores 10 J of energy. (3 points)196x109 kWhe x 1kWhkinetic0.3 kWhe x 3.6 x 106J1kWhkinetic x 1kg • m10 J x 1 gal water3.78 kg water x 1 Niagara fall51 m = 1x1015 gali. Calculate the energy density of each of the above fuels in MJ/kg, and rank them from most to least dense. [Hint: You will need to know the density of oil and natural gas to rank all fuels]. (5 points)From most energy dense to least energy dense Nuclear = 2.7 x 105MWde1000 kgfuel x 24 MWhr1 MWd x 1000 kWh1 MWh x3.6 x 106J1 kWhth x 1 MJ106J= 2.3x107 MJ/kgNatural gas¿3.9 x 107Jm3 x m30.80 kg x 1 MJ106J= 49 MJ/kgOil ¿6.1 x 109Jbbl x 1 bbl159 L x 1 L1kg x 1 MJ106J= 38