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4. (14 points) After a long day working in Gru's Lab, Stuart decides to go sunbathing at the beach and lies on a blanket facing up towards the sun. His skin temperature is 33.C and his total body surface area is 0.4 m. The emissivity of his body is 0.96. The Boltzmann constant o = 5.67x10-8 W/m2K4. Neatly show your calculations to the questions below. e = 0.96 0 = 5. 67 * 108 A = 0.9M 2 TK = 3 30 ( + 273. 15 K = 306.15 1: The power radiated away by Stuart (in Watts) is = COATK Away Prad = (0.94) ( 5.67*10-8) (0. 4ma ) (306. 15) Prod = 76.5 w Bad Math. 10 . 25 Solar radiation falls on Stuart's body with a power per unit area of about 1200 W/m2, but only his top-half is s root exposed to the sun. Assume that he absorbs this radiation with the same emissivity of 0.96. II: The radiative power absorbed by Stuart's body (in Watts) is 0.4 - 0. 2 M2 240 W X 0 ' 96 Heat from sun = 1200W/mo 1200w/ 4 2 xo.ama - atow to.91 leat away = 76.5W @ 330C w x0. 2 = 2 4ow ( half his body is exposed to sun) - 76:5W Txt = 2 40w ( 0,96 ) ( 5 .7 * 10 8 ) ( 6:7 / m ? ) Tx 4 = 2.19 *10 10 loA 240w 1 x = 384.69 Assume that Stuart loses heat only by radiation and not any other method. Ill: As he sunbathes, his body will settle to a final temperature (in Celsius) of 1X390 0 384. 60*- 273. 15*= 111.54 . C