everyday a certain amount of water evaporates from Earth\'s oceans, lakes, and l

Question

everyday a certain amount of water evaporates from Earth's oceans, lakes, and land surface and forms water vapor and clouds in the atmosphere. Everyday a certain amount of rain falls back to earth .Make the reasonable assumptiont that on average, the energy absorbed by the evaporation and lifting of the water is equal to the energy release by its condensation and falling back to earth. The evaporation of one mole of water requires approximately 40.7*10^3 J of heat. An equal amount of heat is released when a mole of water condensed. The annual volume of rainfall on Earth is approximately 5.05*10^5 km^3 and the average cloud altitude is 8.7 km above Earth's surface. How much energy in jouls, is required everyday to evaporate and lift the water?

Explanation / Answer

let's find the moles i n the given volume if water

V = 5.05*10^5 x 10^9 m^3

mass= density x volume = (1000 kg/m^3) ( 5.05*10^5 x 10^9) = 5.05 x 10^ 17 kg

moles = mass/ molar mass = 5.05 x 10^ 17 / 18= 2.805 x 10^ 16

enegry required to evaporate=40.7*10^3 x  2.805 x 10^ 16 = 114.186 x 10^19 J

work done to lift water = FS = mg h =( 5.05 x 10^ 17 kg x 9.8) (8.7 x 10^3) = 430.563 x 10^ 20 J= 43 x 10^ 19 J

total enegy = 157.2423 x 10^ 19 J

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