1Physics 1010:The Physics of Everyday LifeTODAY• Black Body Radiation, Greenhouse Effect2Admin Stuff• Exams are at back of room, alphabetically in fourpiles. Please collect AFTER class• Grades posted on website• Average for exam was ~70%3Black Body Radiation• All bodies radiate according to their temperature• A “black” body is a body that absorbes allradiation incident upon it• Total energy radiated per unit area given byStefan-Boltzmann Law• P = power radiated per unit area = energy radiated per unit time per unit areahttps://solarsystem.colorado.edu4A black body is easy to construct:Consider a a large cavity with a tiny hole drilled into it. Of all the light that goes through the hole, only an insignificantly small amount gets reflected back out. The rest is bounced around the interior of the cavity so many times, that it is finally totally absorbed. The cavity is then a "Black Body".https://solarsystem.colorado.edu/applets/stellarOutput/physics.html5Total Solar Power OutputThe radius of the sun is 696,000km. Its surfacetemperature is 5800K, what is the total powerradiated by the sun?The surface area of a sphere is given by A=4πR2Stefan constant: σ = 5.67*10-8 J K-4 m-2 s-1A) 3.83*1026 W B) 3.83*1030 W C) 3.83*1020 W D) 3.83*1016 W The total power output of a star is call the Luminosity of the star6Total Solar Power OutputThe radius of the sun is 696,000km. Its surfacetemperature is 5800K, what is the total powerradiated by the sun?The surface area of a sphere is given by A=4πR2Stefan constant: σ = 5.67*10-8 J K-4 m-2 s-1A) 3.83*1026 W B) 3.83*1030 W C) 3.83*1020 W D) 3.83*1016 W The total power output of a star is call the Luminosity of the star7Total Power Intercepted by EarthThe Earth circles the sun at 150,000,000km,and its radius is 6400km.What fraction of the sun’s power is incident on the Earth?A) 4.55*10-5 B) 4.55*10-10 C) 4.55*10-15 D) 4.55* 10-208Total Power Intercepted by EarthThe Earth circles the sun at 150,000,000km,and its radius is 6400km.What fraction of the sun’s power is incident on the Earth?A) 4.55*10-5 B) 4.55*10-10 C) 4.55*10-15 D) 4.55* 10-20πRE2/4πRO2 =(1/4)(6400km/150000000km)2=4.55*10-10At the Earth’s distance from the sun, the total solar power is spread over thearea of a sphere of radius 150,000,000km, but the Earth covers only a circleof radius 6400km out of all that area9Total Power Radiated by EarthThe Earth absorbs 70% of the solar powerincident upon its surface. What is the totalpower radiated by Earth?A) 1.22*108W B) 1.22*1011W C) 1.22*1014W D) 1.22*1017W10Total Power Radiated by EarthThe Earth absorbs 70% of the solar powerincident upon its surface. What is the totalpower radiated by Earth?A) 1.22*108W B) 1.22*1011W C) 1.22*1014W D) 1.22*1017W Conservation of Energy: at equilibrium, the Earth has to radiate as much power as it receives from the sun, or else it would either heat up or cool downPout=0.7*Pin=0.7*(4.55*10-10)*(3.83*1026 W)=1.22*1017 W11“Naked” Earth TemperatureWhat would the temperature of the Earth be ifit has to radiate 1.22*1017W, and it had nogreenhouse effect? Tkelvin = Tcelsius + 273A) -18C B) 0C C) 18C D) 32C12“Naked” Earth TemperatureWhat would the temperature of the Earth be ifit has to radiate 1.22*1017W, and it had nogreenhouse effect? Tkelvin = Tcelsius + 273A) -18C B) 0C C) 18C D) 32C13Greenhouse Effect• Sun (5800 oK) radiates mostly at optical wavelengths• Earth (~300 oK) radiates mostly at infraredwavelengths• Greenhouse gasses in atmosphere absorb some IRwavelengths, let others pass to space• Greenhouse gasses re-radiate absorbed energy inrandom direction, so half goes back to the ground.• Overall effect:τ is the greenhouse strength14Greenhouse Effect• For one-layer atmosphere,the incindent power, Is, isabsorbed by the ground.• The ground then radiatesback Ig• Some of Ig gets absorbed bythe atmosphere, and some isallowed to escape• The absorbed power gets re-radiated in a randomdirection, so on average half goes to space andhalf back to the ground• So now we have Is+Ia absorbed by ground, so theground has to have a higher T.15“Greenhouse” Earth TemperatureWhat would the greenhouse strength of the Earth’satmosphere be if it has to radiate 1.22*1017W, and itsAverage temperature is 288 oK? Tkelvin = Tcelsius + 273A) 0.33 B) 0.65 C) 1.35 D) 2.716“Greenhouse” Earth TemperatureWhat would the greenhouse strength of the Earth’satmosphere be if it has to radiate 1.22*1017W, and itsAverage temperature is 288 oK? Tkelvin = Tcelsius + 273A) 0.33 B) 0.65 C) 1.35 D) 2.717“Greenhouse” Venus Temperature• Venus has a multi-layer atmosphere• Each layer increases τ by one• For Venus, τ=121• The temperature of Venus is 3.3 times greater that itwould be without the greenhouse effect (732oK insteadof