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 amount of energy the lake would need to absorb from the Sun to evaporate completely, we need to multiply the specific heat capacity of water by the mass of water in the lake.
The specific heat capacity of water is approximately 4.18 J/g°C (joules per gram per degree Celsius). The lake contains about 4.8 x 10^17 grams of fresh water.
First, we need to convert the mass of water from grams to joules.
Mass of water = 4.8 x 10^17 grams
Specific heat capacity of water = 4.18 J/g°C
Using the specific heat capacity, we can calculate the energy required to heat up the ice to 0°C:
Energy to heat up ice = (Mass of water) x (Specific heat capacity) x (Change in temperature)
= (4.8 x 10^17 g) x (4.18 J/g°C) x (0 - (-3) °C)
= (4.8 x 10^17 g) x (4.18 J/g°C) x (3°C)
= 5.034 x 10^18 J
Next, we calculate the energy required to melt the ice:
Energy to melt ice = (Mass of water) x (Heat of fusion)
= (4.8 x 10^17 g) x (334 J/g)
= 1.6032 x 10^20 J
Lastly, we calculate the energy required to evaporate the liquid water:
Energy to evaporate water = (Mass of water) x (Heat of vaporization)
= (4.8 x 10^17 g) x (2260 J/g)
= 1.0848 x 10^21 J
Adding up the energy required to heat up, melt, and evaporate the ice:
Total energy = Energy to heat up ice + Energy to melt ice + Energy to evaporate water
Total energy = 5.034 x 10^18 J + 1.6032 x 10^20 J + 1.0848 x 10^21 J
= 1.2461 x 10^21 J
Therefore, the lake would need to absorb about 1.2461 x 10^21 joules of energy from the Sun to cause it to evaporate completely.