Solar Voltaic Cells - converting sunlight to electricity over a given area

[jones2767]

Solar Voltaic Cells -- converting sunlight to electricity over a given area

Homework Statement

Lake Mead is formed by the Hoover Dam, and while it actually changes in area and volume, consider it has an average area of 100,000 acres. Assume that 250 W/m^2 of sunlight falls on Lake Mead, how much electricity could be produced if this lake area was covered by solar voltaic cells that convert sunlight directly to electricity with 15% efficiency?

Homework Equations

I'm super confused. I have been working on this problem for about an hour, but I don't even know where to start.

The only equation I can think of to use would be:

F(in) = I x A

Where F is total incoming flux and I is the amount of sunlight??

The Attempt at a Solution

What I have so far is that the Area would be 100,000 acres and the amount of sunlight is 250 W/m^2. I am assuming that I have to find the amount of Watts produced and take 15% of that. Could anyone give me a hint as to how to solve this?

 

[mgb_phys]

1, How many m^2 are there in an acre (hint google calculator)
Once you know how many m^2 and you know that you receive 250W in each m^2 you know the total W

2, Yes you just take 0.15 of the power arriving

 

[jones2767]

So, if there are 4.05 x 10^8 m^2 in 100,000 acres I would then take that number and divide by 250 W/m^2, which would give me roughly 1.61*10^6.

Then I just take the .15 of that?

 

[mgb_phys]

Yes
A tip - carry the units through it helps to make sure you have things the right way around.
Power = w, area = m^2 and light arriving = w/m^2, so if you aren't sure what to divide by what
consider, to get power (W) you must have W/m^2 * m^2 = W

 

[jones2767]

awesome! thank you so much! :)

 

[jones2767]

Wait so I'm dividing the amount of sunlight by the area?
I thought I was dividing the area by the amount of sunlight?
Sorry I took a break in homework before returning to this problem

 

[berkeman]

Wait so I'm dividing the amount of sunlight by the area?
I thought I was dividing the area by the amount of sunlight?
Sorry I took a break in homework before returning to this problem

Carry the units along like mgb advised you to do. The units will help you to figure out what the numerator and denominator should be. Show your work if you want to ask another question.

 

[Phrak]

by the way jones2767, mgb_phys errored slightly with the "yes" remark. So you need to get the units to cancel, leaving Watts, as berkeman says.

 

[mgb_phys]

Sorry didn't chekc your figures,
4.05 x 10^8 m^2 * 250 W /m^2 * 0.15 = 15 GW