446_01c_test4_practice_soln

446_01c_test4_practice_soln - Sample problems for test 4 1...

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Sample problems for test # 4 1) If the ground behaves as a black-body, will the net irradiance between the ground and an overlying cooler cloud be greater if the cloud is a black-body or a gray-body? You can assume that no significant absorption (or scattering or anything else) occurs in between the ground and the cloud. Assume that the temperature of the ground and the cloud is the same in both cases. 0 1 ) ( 1 ) 1 )( 1 ( 1 ) ( 4 2 4 1 2 1 2 1 4 2 4 1 2 1 = = = T T a E a a a T T a a E n n σ σ So, E n will be greater for a black-body (a 2 = 1) than it will for a gray-body (a 2 < 1). 2) If the net irradiance between the 18 o C ground and an overlying cloud is 64 W/m 2 , what is the temperature of the cloud? Assume both the cloud and ground have a reflectance of 0.15. K K T r r r r E T a a a a E T a a T T a a E K m W m W n n n 274 ) 273 18 ( ) 10 67 . 5 )( 15 . 0 1 )( 15 . 0 1 ( )] 15 . 0 )( 15 . 0 ( 1 )[ 64 ( ) 1 )( 1 ( ] 1 [ )] 1 )( 1 ( 1 [ ) 1 )( 1 ( 1 ) ( 4 / 1 4 8 4 / 1 4 1 2 1 2 1 4 / 1 4 1 2 1 2 1 2 2 1 4 2 4 1 2 1 4 2 2 = + + × =
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