Sometimes you come across crazy stuff on the internet. Just check out the Qattara Depression Project; the basic idea is to create a channel to let water from the Mediterranean Sea flow into the Qattara Depression, a giant low-lying area in Egypt. This would create an enormous artificial lake that would change the local climate. It's a prime example of a massive geoengineering project.

The project never got underway, probably because it would be too expensive. But I don't want to talk about the financial or environmental impacts of this project. I want to focus on another aspect of the plan: to use this lake as a method for generating electrical power. Here's how it works. The water from the lake will evaporate and cause a continuous flow of new water from the sea. The moving water in the channel can then be used to turn a turbine and generate electricity. Although someone has already estimated the amount of energy, I want to do this myself. You know ... for fun.

Evaporation

Let's start with the important part—why would a lake lose water? Actually, you can try this yourself. Get some water and put it in a shallow pan. Leave the pan with water on your counter for a couple of days and then check it out. Maybe all the water will be gone, or maybe there will still be some left. But likely there will be less water in the pan than at the start. This is either due to evaporation or you have a cat that came by and drank it. So let's assume that it was evaporation.

Water can exist in three phases: solid, liquid, or gas. During evaporation, some of the liquid water turns into gas phase water (we call this water vapor). But it takes energy to change from the liquid to the gas phase, and the average water particle energy is not enough to move into the vapor phase. However, that's the average energy. Water particles in the liquid phase have a range of different energies. Some water particles are moving slow with low energy and some are moving faster. It's these faster-moving water particles near the liquid's surface that have enough energy to "escape" the liquid phase and evaporate. Of course, if the highest-energy water particles leave, what remains are the lower-energy particles. That means that the average energy (and thus the temperature) of the remaining water decreases. Evaporation is indeed a method to cool stuff.