rature of an object via Wien's law in the case of a thermal spectrum. To predict the power in electromagnetic radiation emitted by an object given its temperature, area, and emissivity. To calculate the equilibrium temperature of a radiating object when the ingoing energy is supplied directly via a power source or absorbed from some external source of radiation. To correctly take into account emissivity and albedo in these calculations. To be able to calculate the intensity (power per unit area) of radiation from a spherically symmetric source given the power of the source and the distance to the source . To calculate the rate of heating/cooling/phase change in situations where heat transfer is taking place via conduction Impres ed sisflu Question 1: Imwe is getting married again, but this time, the wedding is in space! sortw josido ns 10 (see midterm 1, 2019 if you are not already familiar with Imwe) The spacecraft is a spherical shell (R = 5 m) of material whose 9 stell outside surface has emissivity 1 (for infrared wavelengths) and albedo 0.4. The 100 people at the wedding (sorry, Doug) generate a total of w In 100 KW of heat, all of which reaches the surface of the spacecraft. Additionally, the craft absorbs heat from Frozenia's ibet tosido ne star (distance 1010 m, emissivity = 1), whose light has an intensity of 750 W/m near the spacecraft. a) Assuming that the outer surface of the spacecraft has a uniform equilibrium temperature T, determine this temperature. Note: you don't need to worry about inward radiation from the shell, since all of this is absorbed by the shell again. A bos , bejbelts To avenge s nfod 101 An = A.3.) tosido side vd ito bexbold el Jer msed gaimconi end 10 6sis (ayay frail and of islubibasqueq A eviber to delb e bre A zuibsb) Frozenian astronomers measure the spectrum of light from Frozenia's star as shown below. Using this information and the information from part a), determine the radius of Frozenia's star. Intensityhom bis nottalbot anivovitaldong dtiw ebilobig ance jag Ilov sea howemod aids my wellble andjosue sniwollot ent golevab Joy glad Hiw eids agod sw ale naiW aly tooldo ne to atureregmist ard andlowbeb bris andignelovew muitoage 400 800 1200 1650 + 1 ( mm ) I endi nard mosido anifsibsa's to olufsneginet mutidifiups and stelualso aT of noisiest to sowes ismate emoa mail bed feared laughswon 5 elviebomb beilaqua Tips: ecnude end of sonsfell add bris son be ends to jewon aids nevin sotobe sittemmy? The thermal radiation from an object with temperature T has a peak wavelength of 1 = b/T, where b = 2.9 mm-K For an object whose temperature is not changing, we have Hnet = 0, or Hin = Hout. This is just energy conservation. isfilms? Ybestis son ers voy istbim Objects with temperature T radiate energy from their surface at a rate H = A e o T4. The area A is the total surface area of the part of the object at temperature T. The emissivity e is a property of the surface material. .NO obacite If the object is in an environment with temperature Tenv, it will absorb radiation at a rate H = Aeo (Tenv)4 For an object radiating with power H uniformly in all directions, the intensity or power per area of the radiation at a distance R from the object is I = H/(4 It R2). The relative intensity at two different distances is then determined by 12/11 = (R1/R2)?. The solar constant Isc is defined to be the intensity of sunlight in the vicinity of the Earth. misish For an object in radiation with intensity I coming from a distant source, the amount it will absorb is H = Al (1 - a), where a is the albedo or fraction of light reflected, and A here is the area of the incoming beam that is blocked off by the object (e.g. A = It R2 for both a sphere of radius R and a disk of radius R perpendicular to the light rays)