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............................................... Topics in Physics:

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1. The Sun’s Energy Output

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The Solar Constant Check yourself: Does everyone know what a watt (W) is? A milliwatt (mW)? We call this number “The Solar Constant” and designate it by the Greek letter sigma ( ). When we measure the midday intensity of sunlight at the Earth’s surface, we find that about 136.7 mW fall on every square centimeter. At 1 A.U.: = 136.7 mW/cm 2.

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A watt (W) is a unit of energy flow - Joules per second. A milliwatt (mW) is 10 -3 W. Does everyone know what an “A.U.” is?

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An A.U. is the average Earth-Sun separation, ~ 150,000,000 km. 1 A.U.

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Questions: If the mean distance from the Earth to the Sun is 1.5 10 8 km, and the solar radius is 1.4 10 6 km, then 1. What is the value of the solar constant P at the photosphere, i.e., the sun’s visible surface?

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1 A.U. The same amount of energy per unit time passes through the photosphere as through a sphere with radius 1 A.U. Answer to Question #1: = 136.7 mW/cm 2 @ 1 A.U. r Sun = 1.4 X 10 6 km 1 A.U. = 1.5 X 10 8 km p = ?

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Answer to Question #1 Continued: a. Dimensionally: Energy per Unit Time = (Area) ~ 1.6 10 6 mW/cm 2 b. Conservation of Energy: P ( Photosphere Area ) = ( 1A.U. Sphere Area ) c. Solving: P = 136.7 mW/cm 2 (1.5 10 8 km/1.4 10 6 km) 2 4 (r p 2 )( P ) = 4 (r 1A.U. 2 )( ) P = (r 1A.U. /r P ) 2 Area of a Sphere = 4 r 2.

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Questions (continued): If the mean distance from the Earth to the Sun is 1.5 10 8 km, and the solar radius is 1.4 10 6 km, then 2. What is the total energy output per unit time of the sun in W?

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Answer to Question #2: a. Dimensionally: Total Energy per Unit Time = p (Total Surface Area of Sun) 390 Trillion-Trillion Watts ~ 3.9 10 29 mW = 3.9 10 26 W b. Reminder: Area of a Sphere = 4 r 2 c. Solving: With r Sun = 1.4 10 6 km = 1.4 10 11 cm, (1.6 10 6 mW/cm 2 ) 4 (1.4 10 11 cm) 2.

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Question #2 Continued: If an average American city has a peak power consumption of 500 MW, estimate how many average American cities this total energy output (390 trillion-trillion watts) is equivalent to. 1 MW = 10 6 W

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About 780,000 trillion average American cities! 3.9 10 26 W 5 10 8 W/Avg.City ~ 7.8 10 17 Avg.Cities Question #2 Continued:

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Question #2 Continued Again: Estimate how much of this total energy output is actually intercepted by the Earth. Hint: r E = 6,400 km

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Question #2 Continued Yet Again: a. Dimensionally: Energy Intercepted at Earth = Cross Section of Earth = r 2 180,000 trillion watts, enough to run almost 360 million average American cities! ~ 1.8 10 20 mW = 1.8 10 17 W b. Solving: 136.7 mW/cm 2 (6.4 10 8 cm) 2.

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Question #2 is finished at last!!! #2 Continued: 1.) Dimensionally: Energy Intercepted at Earth = Cross Section of Earth = r 2 180,000 trillion watts, enough to run almost 360 million average American cities! ~ 1.8 10 20 mW = 1.8 10 17 W 2.) Solving: 136.7 mW/cm 2 (6.4 10 8 cm) 2 Question #2 is finished at last!!!.

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Questions (Continued): If the mean distance from the Earth to the Sun is 1.5 10 8 km, and the solar radius is 1.4 10 6 km, then 3. In what form is this energy transmitted into space?

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Answer to Question #3: The energy is transmitted as light (or, more properly, electromagnetic radiation).

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2. Harnessing the Sun’s Energy

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Question: How can we harness the energy from the sun?

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Some possibilities are: Solar thermal collectors Solar dynamic systems Solar cells

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What are Solar Cells? 136.7 mW/cm 2 A solar cell is a solid-state device that directly converts sunlight into electricity. + -

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What is the most common raw material from which solar cells are made? The most common raw material is white sand, specially refined to remove unwanted impurities.

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+ “Refining” Sand: Can you fill in the blanks? Words + Chemical Symbols + Silicon Dioxide SiO 2 Silicon Si Oxygen O2O2 Si O O O O

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Reflected light SOLAR CELL V oc Energy absorbed from incident sunlight electrically excites the solar cell to produce a voltage. For silicon, V oc ~ 0.5 V Absorbed light Incident sunlight

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Load I When a load is placed across a solar cell, electrical power is delivered to the load. +V-+V- Power = Current Voltage = I V +_+_

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Questions: 2. Is all of the energy absorbed by the solar cell converted into electricity? 3. If the answer to Question #2 is, “No,” then what other energies might be involved? 1. Is all of the sunlight falling on a solar cell absorbed?

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Answer to Question #1: No. Some of it is reflected back into space. Answer to Question #2: No. Silicon solar cells are nominally 20% efficient. Answer to Question #3: The rest of the energy goes into heating the solar cell.

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Problem: A given circular solar cell has a 1 cm radius. It is 18% efficient. Because today is cloudy, the solar constant is a mere 97 mW/cm 2. What is the maximum power output you can expect from the cell?

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Answer: The cell area (collecting area) is r 2 = cm 2 If the cell were 100% efficient, it would produce (97 mW/cm 2 ) ( cm 2 ) But because it is only 18% efficient, it produces ~ 305 mW 305 mW 0.18 = 55 mW.

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3. Using Solar Power

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Question: Now that you know something about harnessing the sun’s energy with solar cells, where do you suppose we can put that energy to work?

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Earth’s Surface Earth Orbit Solar System Mars

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Do you have any questions or topics you would like to discuss?

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For those interested in talking more, contact me at: joseph.c.kolecki@grc.nasa.gov

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