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
To calculate the total amount of energy required for the lake to evaporate completely, we need to multiply the specific heat of water (3109 joules) by the mass of water in the lake (4.8 x 10^17 grams).
Therefore, the calculation would be:
Total energy = (3109 J/g) * (4.8 x 10^17 g)
= 1.49 x 10^21 J
So, the lake would need to absorb approximately 1.49 x 10^21 joules of energy from the Sun to evaporate completely.
To calculate the amount of energy needed for Lake Erie to evaporate completely, we can follow these steps:
1. Determine the specific heat of water: The specific heat of water is the amount of energy required to raise the temperature of 1 gram of water by 1 degree Celsius. In this case, the specific heat of water is given as 721.5 calories/gram.
2. Convert specific heat to joules: To convert calories to joules, we can use the conversion factor of 1 calorie = 4.184 joules. So, the specific heat of water is 721.5 calories/gram x 4.184 joules/calorie = 3018.156 joules/gram.
3. Calculate the total energy required: Multiply the specific heat of water by the mass of water in Lake Erie. The mass of water in Lake Erie is given as 4.8 x 10^17 grams.
Total energy needed = (3018.156 joules/gram) x (4.8 x 10^17 grams) = 1.45 x 10^21 joules.
Therefore, the lake would need to absorb approximately 1.45 x 10^21 joules of energy from the Sun to evaporate completely.