[rlee05]

When it rains an inch of rain, it means that if we built a one inch high wall around a piece of ground that the rain would completely fill this enclosed space to the top of the wall. Rain is water that has much been evaporated from a lake, ocean, or river and then precipitated back onto the land. How much heat, in kJ, must the sun provide to evaporate enough water to rain 1.0 inch onto 1.0 acre of land?

1 acre = 43,460 ft²

 :delta:H_vap for water is 44 kJ/mol

Assume density of water is 1g/cm³


Any help will be greatly appreciated! 

[sjb]

What volume of water do you need to evaporate?

[rlee05]

I'm sorry but I don't know.  I have never had to work a problem quite like this before, and I have put all of the information that my teacher gave us.
So I just know that the sun will have to "evaporate enough water to rain 1.0 inch onto 1.0 acre of land"

[sjb]

OK, what if the question had said a field 100 x 100 m, and 10 cm of rain? What's a definition of volume?

[rlee05]

I know volume is the amount of space something occupies.
Also, I know in chemistry I usually find volume using V=m/d, and I have the density of water so am I going to be using that formula to find the volume?
It is starting the click for me a little bit, but I'm still trying to have that "Ah ha" moment so thank you for helping me 

[sjb]

What's the volume of, say, a cereal packet, like this one (by which I mean, how do you calculate it, I'm not looking for a number as such)? http://upload.wikimedia.org/wikipedia/en/thumb/e/e6/ShreddedWheat.jpg/180px-ShreddedWheat.jpg

(Bear with me)

[rlee05]

Oh, I'm sorry.  My mind wasn't even thinking about using volume in that way.
So volume is equal to length x width x height.

[sjb]

Yes, or alternatively, if it were an irregular prism, cross-sectional area x height.

Now, you have a measure of area in your original problem, and a height, so what's the volume of water falling on your land? You may find it easier to convert figures to metric, so 1 inch is 2.54 cm, and one acre is, well, I'll let you do that

Once you have the volume you can then use the density of water to calculate the mass of water falling, and consequently the number of moles falling.

You then have the amount of heat it takes to vaporise 1 mol of water, and the number of moles, so Robert is your parent's male sibling, no?

[rlee05]

Thank you so much!

I am going to show you the answer I got and how I got it.  If you see that I did something incorrectly, would you mind telling me?

Volume:

Height = 1 inch = 2.54cm
Area = 43,460 ft² x (144 in²/1 ft²) X (6.4516 cm²/1 in²) = 40375561.18 cm²

Volume = area x height
Volume = 40375561.18 cm² x 2.54 cm = 102554179.4 cm³ (

Mass:

Mass = Volume x Density
Mass = 102554179.4 cm³ x 1 g/cm³ = 102554179.4g

Grams to moles:

102554179.4g H₂O x (1mol H₂O/18.01g H₂O) = 5694290.92 moles H₂O

Heat:

5694290.92 moles H₂O x (44kJ/mol) = 250548800.3 kJ

I have not yet taken significant figures into account.
Please let me know if I am missing a step or if I am completely off.

Thanks again!

[sjb]

Looks about right to me!