Question

At our distance from the Sun, the intensity of solar radiation is 1370 W/m2. The temperature of the Earth is affected by the greenhouse effect of the atmosphere. This phenomenon describes the ef- fect of absorption of infrared light emitted by the surface so as to make the surface temperature of the Earth higher than if it were airless. For comparison, consider a spherical object of radius r with no atmosphere at the same distance from the Sun as the Earth. Assume its emissivity is the same for all kinds of electromagnetic radiation and its temperature is uniform over its surface. (a) Explain why the projected area over which it absorbs sunlight is ter and the surface area over which it radiates is 4ter? (b) Compute its steady-state temperature. Use Known Values sense-making to determine if this a reasonable value? (c) Why would an increase in greenhouse gasses such as water vapor, carbon dioxide, and me thane be cause for alarm?

Answer 1

Answer.- Solar rediaton at earthh Intewaily = 1370 W/m². Projected overwhich eo Earth absorbs Sun light area See that projectlon of easly of earth hemisphes is TER md ever which figue From the we can Curved area light faels . is the Thisg area But when earth Radiales it works as black body . So it from every pant crea: which is Surface area of emits yadiation of the cuued earth. which is 4-TT R.

5steady State Temperatine state evergy steady gainal by earthisequal to At energy dostby earth. Total energy gin that arrives at earth's second per Energg gam metei is 137oW/m² "Sunface per But some fraction of it gets seflected by to Space which is albedo of earth. o heat gain by earth is Hence toted 1370 W (1-e) per se cond per meter?. Hence heat gun by earthe rom Sun 1370W (1-~) .TTR. me Let 'T' be the temperature of earth hence heat emitted y earth at Steady state - 1390 W

1370 W/m' (1-«) ( ats albedə of earth) 0.3 1370 Whr (1-0.3) 4 x S.67X10° w k* 255.002170 k 255 k T= (255-275)°C -18°C below the average Empraline of earth () (~15) This because ve have nat taken into account the greenhrouses, which absorbs heat and increase the temperature· Green house gasses absorb heat from * increase the temperature of earth. Tub will Cause Global Warming. Due to which iceat poles light and Sun melt and increase Will the make low altitude countries hand for sunvirl, sealevel. Which will AbsotkerS