Lake Erie contains about 4.8 x 10^17 grams of fresh water. Assume that the lake has frozen solid and that the ice starts off at -3 C. How much energy would the lake need to absorb from the Sun to cause it to evaporate completely?
Each gram of water will require 721.5 calories to heat up, melt and evaporate. That equals 3109 joules. Multiply that by the mass of water in the lake.
(724.4c)(4.8 x 10^17) = 3.46 ^20
Is this correct?
Yes, your calculation is correct. To find out how much energy the lake would need to absorb from the Sun to evaporate completely, you need to multiply the specific heat capacity of water (721.5 calories/gram) by the mass of water in Lake Erie (4.8 x 10^17 grams).
To convert calories to joules, you can use the conversion factor 1 calorie = 4.184 joules. Therefore, each gram of water requires 721.5 calories x 4.184 joules/calorie = 3019.656 joules.
Now, multiplying this by the mass of water in Lake Erie (4.8 x 10^17 grams) gives:
3019.656 joules/gram x (4.8 x 10^17 grams) = 3.46 x 10^20 joules
So, the lake would need to absorb approximately 3.46 x 10^20 joules of energy from the Sun to evaporate completely.