# Why doesn't the rain violate the law of conservation of energy?

## Main Question or Discussion Point

When the water receives energy from the sun, the water on the surface will have an increased temperature and may evaporate and float up to form clouds.

This seems like common sense but where did the water gained the gravitational potential energy?

The increased temperature the water has must be dissipated back into the atmosphere to match the ambient temperature in the exact ratio of 1:1, since heat cannot be converted into gravitational PE (Or can it?). So why doesn't this violate the conservation of energy?

Please enlighten me on how this works.

Thanks.

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## Answers and Replies

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russ_watters
Mentor
Um, did you even read my question? We all know that water gets the energy from the sun. However, that doesn't explain where the gravitational potential energy comes from. The energy the water receives is dissipated into the air either through conduction, convection, or radiation.

Now compare it with a piece of metal or wood exposed to the sun in the open. The object will release the energy it obtains from the sun through conduction and radiation. The same must apply for the water, but yet the water is still somehow left with an extra energy from the GPE.

For your information, clouds can weigh up to a million tons so the extra energy from the GPE must come from somewhere.

Water vapor is less dense than dry air, so it rises clouds are just bunches of water vapor. When it gets high enough, the temperature is low enough for it to condense and form rain. This process is entirely driven by the sun.

The sun's energy allows the water to make the phase transition. The water does not radiate.

russ_watters
Mentor
....and the link I posted explains the process in detail.

Yes, but consider a water trapped inside a sealed jar. If we heated the water the water will transform into steam but if left for a while, the heat we put into the jar will be released back out of the system in one form or another and it must equal the exact energy we put into the jar.

I also understand that it steam is less dense than the air but if you could measure the energy input vs the output of the water, wouldn't the output be more than the input since the energy the water release into the atmosphere MUST equal the energy the sun has put into it?. The number just doesn't add up.

For example,

Input: 100 joules of heat

Output: 100 joules of heat + 40 Joules of GPE

This obviously doesnt make sense.

Yes, but consider a water trapped inside a sealed jar. If we heated the water the water will transform into steam but if left for a while, the heat we put into the jar will be released back out of the system in one form or another and it must equal the exact energy we put into the jar.
And the steam will turn back to water so energy was conserved.

I also understand that it steam is less dense than the air but if you could measure the energy input vs the output of the water, wouldn't the output be more than the input since the energy the water release into the atmosphere MUST equal the energy the sun has put into it?. The number just doesn't add up.

For example,

Input: 100 joules of heat

Output: 100 joules of heat + 40 Joules of GPE

This obviously doesnt make sense.
It doesn't output 100 joules of heat. The individual molecules need that kinetic energy to stay in the gaseous phase.

....and the link I posted explains the process in detail.
It explains the process but it doesn't explain the physics behind it... The numbers just doesn't add up, please look at my post above.

And the steam will turn back to water so energy was conserved.
Yes that is exactly my point, the steam turns back into water so where does the extra GPE come from?

It doesn't output 100 joules of heat. The individual molecules need that kinetic energy to stay in the gaseous phase.
[STRIKE]What? What does have to do with kinetic energy?[/STRIKE]

Nvm, I get what you mean. I understand that each molecule needs energy to stay in the gaseous phase but the energy must be released after it becomes droplets of water. It doesn't really matter if the energy is "stored" before and released afterwards.

So I am still confident that the heat output must = the heat input into the water molecules.

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1. Sun transfers some energy to water molecules allowing them to escape the large body and be called a gas.

2. The water vapor is less dense than dry air so it rises.
-Think about the water vapor molecules being like little stones. Since they are in a "sea" of a fluid (dry air) they are less dense than, they float to the top like buoys.

There's no extra energy, if you like you can say as soon as the water made it to the gas phase, there was a buoyant force pushing it upwards and you can call the energy it got gravitational potential energy.

3. As it gets higher in the sky the temperature (measure of the average kinetic energy of the molecules in the gas) and pressure decrease, and it make the transition back to the liquid phase, which is more dense than air so it falls back down.

I think it's safe to conjecture that most elementary difference between the phases of matter is how close the individual particles are together and how they move. The equation of state for a gas always involves the overall pressure, volume, and temperature.

The water vapor is less dense than dry air so it rises.

There's no extra energy, if you like you can say as soon as the water made it to the gas phase, there was a buoyant force pushing it upwards and you can call the energy it got gravitational potential energy.
Well, this violate the conservation of energy.

Consider my previous example:

Input: 100 joules of heat

Output: 100 joules of heat + 40 joules GPE

This obviously doesnt make sense.

PS: I perfectly understand the process of the water cycle. What I don't understand is why doesn't the number above add up.

Your example is incorrect. Do you understand the connection between force and energy?

If you put a cork in a bowl of water it will want to rise. There is a force pushing upwards called the buoyant force. If nothing opposes it, it will continue to rise until it cancels with the force on the cork due to gravity. At this equilibrium point, it has a greater gravitational potential energy relative to where it was at the bottom of the bowl. All the "buoyant potential energy" it had is now "gravitational potential energy." It obviously had some potential energy at the bottom at the bowl because when you let go, it moves up, just like if you hold a rock in the air and let it go it moves because it had gravitational potential energy.

Just replace cork with a water molecule and the bowl of water with the air and now you know why the vapor rises.

Also I feel like this discussion is hovering around the question "what is potential energy?" Potential energy can often be transformed away by choosing different references. For example, you could say a rock sitting on a table has no gravitational potential energy relative to the table. Now it has some PE relative to the ground, but why doesn't it fall? Because the normal force exerted by the table cancels the gravitational force. Same with the cork and the water. Same with water vapor sitting high in the sky on top of the regular air.

russ_watters
Mentor
The number just doesn't add up.

For example,

Input: 100 joules of heat

Output: 100 joules of heat + 40 Joules of GPE

This obviously doesnt make sense.
When the water vapor rises, the pressure drops and it cools. That's why it condenses.

See: http://en.wikipedia.org/wiki/Adiabatic_process

Your example is incorrect. Do you understand the connection between force and energy?

If you put a cork in a bowl of water it will want to rise. There is a force pushing upwards called the buoyant force. If nothing opposes it, it will continue to rise until it cancels with the force on the cork due to gravity. At this equilibrium point, it has a greater gravitational potential energy relative to where it was at the bottom of the bowl. All the "buoyant potential energy" it had is now "gravitational potential energy." It obviously had some potential energy at the bottom at the bowl because when you let go, it moves up, just like if you hold a rock in the air and let it go it moves because it had gravitational potential energy.

Just replace cork with a water molecule and the bowl of water with the air and now you know why the vapor rises.

Also I feel like this discussion is hovering around the question "what is potential energy?" Potential energy can often be transformed away by choosing different references. For example, you could say a rock sitting on a table has no gravitational potential energy relative to the table. Now it has some PE relative to the ground, but why doesn't it fall? Because the normal force exerted by the table cancels the gravitational force. Same with the cork and the water. Same with water vapor sitting high in the sky on top of the regular air.
I understand that there is buoyant force acting against the water vapor, causing it to rise and perfectly understand the concept of GPE.

However, what I don't understand is that the GPE of the water vapour, relative to the ground, when added with the energy dissipated to the air is MORE than what it receives from the sun.

Please explain as to why the output appears to be more than the input in this particular system. Not why it rises, or how GPE works because I am confident that I perfectly understand these concepts quite well.

russ_watters
Mentor
However, what I don't understand is that the GPE of the water vapour, relative to the ground, when added with the energy dissipated to the air is MORE than what it receives from the sun.

Please explain as to why the output is more than the input in this particular system.
It. Isn't.

When the water vapor rises, the pressure drops and it cools. That's why it condenses.

See: http://en.wikipedia.org/wiki/Adiabatic_process
I'm sorry but I don't understand how this relates to my question

Could you please explain what you mean by that?

It. Isn't.
Then where does the GPE come from? You mentioned something about condensation but I don't understand how it relates to my question...

However, what I don't understand is that the GPE of the water vapour, relative to the ground, when added with the energy dissipated to the air is MORE than what it receives from the sun.
It isn't.

The water doesn't dissipate all its energy to the air.

The change in gravitational potential energy that is added is the same buoyant energy that was lost.

The sun energy provides the phase transition energy. When it's up high, pressure decreases, to temperature decreases, so average kinetic energy decreases, so the molecules are closer, so they become a liquid instead of a solid.

Bottom = Sun + Buoyant
Top = Gravity + "Heat"

Gravity = Buoyant

It isn't.

The water doesn't dissipate all its energy to the air.

Gravity = Buoyant
I believe it must eventually does, due to entropy.

It isn't.

The change in gravitational potential energy that is added is the same buoyant energy that was lost.

The sun energy provides the phase transition energy. When it's up high, pressure decreases, to temperature decreases, so average kinetic energy decreases, so the molecules are closer, so they become a liquid instead of a solid.

Bottom = Sun + Buoyant
Top = Gravity + "Heat"

Gravity = Buoyant
This made sensed. So basically are you saying that the water vapor replaced other molecules in the air, which therefore lost the GPE in exchange, therefore conserving the energy?

I believe it must eventually does, due to entropy.

This made sensed. So basically are you saying that the water vapor replaced other molecules in the air, which therefore lost the GPE in exchange, therefore conserving the energy?
Well I don't think you should discuss entropy if you don't understand adiabatic processes...

No. I'm saying the buoyant potential energy was converted to gravitational potential energy. (And I'm really abusing the language here, it's hard to explain without resorting to thermodynamics) If I were saying what you were saying, how can you account for the different masses of the particles? An H2O gas is less dense than a Nitrogen or an Oxygen gas.

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cjl
Science Advisor
I'm sorry but I don't understand how this relates to my question

Could you please explain what you mean by that?
As the water vapor rises, it expands and cools adiabatically. This cools the water down, but no heat is released to the surrounding atmosphere. So, the water does not release as much heat as it took in initially, because some of the cooling occurs due to this adiabatic expansion. Also, as the water vapor is rising, other gas molecules are descending, and the descending mass of gas is greater than the rising mass of water vapor (pretty much by definition, or the water vapor would not be buoyant in the atmosphere).

Dale
Mentor
This seems like common sense but where did the water gained the gravitational potential energy?
By lowering the dry air's GPE.

The sun gives energy to the water, causing it to evaporate. The water vapor displaces the column of air above it which therefore gains GPE. Then the denser dry air goes "downhill", displacing the vapor upwards, reducing the overall GPE and causing wind etc.