Evaporation and Potential Energy

A barrel full of gasoline was carried from the ground level to the tenth floor. Sure it has potential energy. After some time, all the gasoline has evaporated. What has happened to the potential energy? Hope it is a legitimate question? Many thanks, Kind regards, Victor
- Victor (age 67)
Haifa, Israel

If you think about where the molecules of gasoline go when they evaporate, on the average they go up, even from the 10th floor. So the gravitational potential energy goes up even further when they evaporate. Also, there's some negative interaction energy between them in the liquid, so that chemical energy also goes up as they evaporate.

Where does all this energy come from? It's pulled out of the thermal energy in the gasoline and its surroundings. That's usually mostly energy of little sound vibrations, about half kinetic and half potential. So the net potential energy goes up a bit and the net kinetic energy goes down the same amount.

The process is driven by the entropy gained by the gasoline molecules running around in the large space of the atmosphere. That's more than the entropy lost by pulling the thermal energy out of the little vibrations, etc.

Mike W.

(published on 03/27/2013)

Hi Mike - many thanks for the prompt answer of yours. This was my question: "A barrel full of gasoline was carried from the ground level to the tenth floor. Sure it has potential energy. After some time, all the gasoline has evaporated. What has happened to the potential energy? Hope it is a legitimate question? Many thanks, Kind regards, Victor" ===================================================== Now, after receiving your answer, I would like to detail and deepen my question. Let's say that the empty barrel is weightless and that the gasoline is weighing 200 Kg. By dropping that barrel from the 10th floor on a car, I penetrate the car's roof and make all the four tires to explode. However when if I come after a certain time and I find the barrel empty I can't use that potential energy! Where is it? Thank you!
- Victor (age 67)
Haifa, Israel

Hello Haifa,
This is Lingyi and I'll try to answer your question. We see that as the barrel sits there for a long time, its entropy increases as the gasoline evaporates. And the idea here is that when all the gasoline is gone, its gravity potential energy doesn't disappear, but instead becomes unusable. This is often what people say about the second law of thermodynamics. So there is really nothing wrong with the energy of the gasoline. It's the amount of energy that's available to you in the barrel that changes.
Hopefully this answers your question.
Lingyi

 

Just to clarify- That potential energy had gone up, but the entropy went up a whole lot too. The "usable" energy here is approximately the Helmholtz free energy G=U-TS, where U is the net energy of the system, T is the absolute temperature of the environment, and S is the system entropy.  The point here is that S goes up so much that G ends up going down, even though U  increase. So there's less available free energy.  (There are some complications involving pressure, volume, and the mixing with the atmosphere, but the simplified version here gets at the main idea.) Mike W.

(published on 04/02/2013)