Thermodynamics – Is the Law of Conservation of Energy Broken by Heating and Cooling a Liquid?

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Let's say there's a puddle of water on the ground. I use a magical device to give it enough thermal energy to vaporize into water vapor. The water vapor floats up into the sky. I then use the magical device to absorb the same amount of thermal energy I previously gave it. The water vapor then condenses to water and falls back on the ground and forms the same puddle of water on the ground.

My device absorbed and gave the same amount of energy, therefore the net energy in the system should be the same. However, it seems like the system's energy should increase from the water vapor floating up into the sky and producing thermal energy from friction with the air molecules. It should also produce more energy from friction with the air when it falls as rain drops towards the Earth and also when it hits the ground and disperses more thermal energy from its kinetic energy.

This breaks the law of conservation of energy, but I don't see what's wrong with my model. I thought about this when I read that the rain produces a lot of thermal energy from friction with the air.

Best Answer

The first device is not so magical - you can accomplish the same result with a fire under a pot. The second device, on the other hand, is indeed magical: you are converting heat into usable energy without any side effects. This is prohibited by the second law of thermodynamics.

You are also violating the first law, though, and the thermodynamics police are coming for you ;)

The problem lies in making an unwarranted assumption. The vapour rises in the air, and you say you want to consider effects such as "friction", or the exchange of heat between water and other air molecules. A proper description of this phenomenon will show that any energy gained by the air is lost by the water, so when you activate your second-law-violating device the vapour will yield less energy than what you put in initially - unless, of course, you are also able to retrieve the energy which was lost to the air.

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