ELEN280 MECH287 Fall 2023 Homework #1

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Santa Clara University *

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Mechanical Engineering

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Jan 9, 2024

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SCU ELEN280/MECH287 FALL 2023 Homework Set #1 10/11/2023 1. Study the diagram below. It can be found on the web at: https://flowcharts.llnl.gov/content/assets/images/energy/us/Energy_US_2016.png a. Which source of energy currently contributes the smallest fraction to electricity generation? How much and to what categories does it contribute? Currently, geothermal energy contributes the smallest fraction to electricity generation. Out of the total energy consumption of 97.3 quads, geothermal contributed a total of 0.23 quads; 0.16 quads towards electricity generation, 0.04 quads toward residential, and 0.02 quads toward commercial use. b. How much electrical energy is used for transportation? What are the sources of energy for transportation? 0.03 quads of electrical energy was used for transportation, of which sources include petroleum (25.7 quads), biomass (1.43 quads) and electricity (0.03 quads).

2. Redo the problem in Solution Box 4.8 of the text. This time let’s consider the planet Mars. a. Determine the amount of solar flux that would be expected for Mars that is 228,000,000 km away from the Sun rather than 150,000,000 km away from the Sun as Earth is. Use the mean radius of Mars as 3390 km and that of the Earth as 6370 km. Give your answer in W/m 2 . S = S 0 ( R 0 R ) 2 = 1370 ( 1 1.52 ) 2 = 592.97 W / m 2 b. What is the equilibrium temperature of Mars in 0 C? It has no atmosphere. Use same basic assumptions that are given in SB4.8 including  = 0.31. Equilibrium = T = ( S ( 1 − α ) 4 σ ) 1 / 4 α = 0.31 σ = 5.67 x 10 − 8 W / m 2 S = 593 W / m 2 T = ( 593 ( 1 − 0.31 ) 4 ∗ 5.67 x 10 − 8 ) 1 / 4 T = 206 K =− 67 ℃

3 . Assume that you use 30 kWh total of electric power per day at your house. Your gasoline-powered car averages 22 miles per gallon and you drive an average of 70 miles per day. (assume these numbers apply to all seven days of the week.) a. Which is a larger amount of energy, what you use for your house or for your car? By how much? House: Energy = 30 ( kWh day )( 7 days week ) ( 3.6 ∗ 10 6 J kWh ) = 7.56 ∗ 10 8 J / week Car: Energy = ( 70 miles 1 day )( 7 days 1 week )( 1 gallon 22 miles ) ( 1.32 ∗ 10 8 J 1 gallon ) = 2.93 ∗ 10 9 J / week Difference : 2.93 ∗ 10 9 J week − 7.56 ∗ 10 8 J week = 2.18 ∗ 10 9 J week Therefore, the car uses more energy, by about 2.18 ∗ 10 9 J week . b. Electricity to your home and transportation fuel are only two of the ways that you consume energy. What are some of the others? Name at least two. (For at least one of them the majority of the power should be consumed away from your house.) (I am not asking for sources of energy or types of energy generators, I am asking for the other major ways that you consume energy besides electricity, natural gas, and gasoline.) Battery power is also used in many homes, as well as vehicles these days. Aside from powering electric vehicles, they also power many devices within the home such as clocks, remotes, flashlights, and security cameras as well. Another source of energy is heat, powered from wood and/or coal. Many a time I have started a fire using wood and/or coal to prepare my meals, outside, away from my home.

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4. Inertial Confinement Fusion Energy Production The $5B (construction cost) National Ignition Facility (NIF) at Lawrence Livermore National Lab promised to “ignite” a thin layer of DT (deuterium-tritium) ice fuel in a 2mm capsule using a bank of 192 20-inch square glass lasers focused on the target. Assume:  the electricity used initially was produced at a fossil-fuel (as primary-energy) power plant and delivered to the NIF at 33% overall efficiency  the electricity delivered to the NIF is used with 1% efficiency to produce laser light that impinges on the target (in reality it is much less efficient)  the energy output from the fusion reaction and burning of the DT is 1.4X the amount of energy in the impinging laser beams, i.e. 140% efficiency.  the heat from the fusion process is then recovered and used to run a Carnot cycle steam process to produce electricity at 33% overall efficiency a. What is the energy efficiency of the whole system as an energy generation system? Start from the fossil-fuel primary-energy used at the electric power plant supplying the NIF and end with the electrical energy coming out of the NIF. Energy Efficiency = 0.3 ( 0.05 ) ( 3 ) ( 0.33 ) = 0.01485 = 1.485% b. Let’s say you can increase the efficiency of the laser light production from electricity to 40%. How much would you need to increase the efficiency of energy production for the fusion reaction to get 100% efficiency overall for the whole system (from primary fossil-fuel energy to electrical energy leaving the NIF)? They are calling this engineering breakeven. Efficiency = 100% = 1 = 0.3 ( 0.4 ) ( x ) ( 0.33 ) x = 1 0.3 ( 0.4 ) ( 0.33 ) = 25.25 = 2525% Therefore, if the efficiency of the laser light production from electricity is 40%, the energy production efficiency factor would have to be 2525% in order to achieve 100% overall energy efficiency of the whole system.

5. Choosing the Right Problem-Solving Language A monk wants to visit a monastery at the top of a mountain. There is only one path up the mountain and he will take one full day for the ascent and a second full day for the decent so he can enjoy the view. When he climbs up the trail he starts at sunrise, stopping and resting whenever he feels like it, but when he is in motion he is always ascending. He arrives at the monastery around sunset. When he comes down the mountain he again leaves at sunrise and again stops whenever he wants, but is always descending when in motion. He again arrives at his destination around sunset. (Adapted from James Adams, Conceptual Blockbusting ) Question: Is there a time of day when the monk is at the same position on the trail on both days? (Just saying yes or no is not an acceptable answer. Present some kind of proof or argument either way.) Given the fact that on the first day the monk ascends the mountain at sunrise and reaches the monastery at sunset, as well as the fact that on the second day he descends the mountain at sunrise and reaches the bottom at sunset, we can say that yes, there could potentially be a time of day when the monk is at the same position on the trail on both days, given a few assumptions: Sunrise: 6am Sunset: 6pm Since it takes the monk the same time to ascend and descend, and we assume the breaks he takes are at the same relative time periods of travel, and that he has the same velocity ascending and descending, then we can assume that he is at the same position on the trail on both days at around 12 noon. (6 hours halfway point). However, if he takes all his breaks in the second half of the ascent, and none in the first half, and takes all his breaks in the second half of the descent and none in the first, that may skew the reality of his position.