2nd law of thermodynamics and gravity

If I have a container with gas according to my understanding of 2nd law of thermodynamics molecules/particles will not be at one side of the container but if the container gets energy from outside molecules can be in such state.

I'm trying to understand how gravity is affecting such container.

If you place a container on the surface of the Earth gravity will change the pressure distribution of the gas in the container. This means there will be constantly more molecules at the bottom side of the container than the top side.

For an observer inside the container this would suggest there must be energy from outside responsible for this.

So in this case is gravity the source of this energy? If yes how long does it last?

Thinking along these lines if you have a theoretical container with a wall in the middle and both "chambers" are filled with gas. The container is floating in space. Once the gas cooled down wouldn't gas molecules be more likely to be found near the inner wall due to gravitational pull from matter in the other chamber?

3 Answers

As has been pointed out, the gas molecules in the container would be evenly distributed per the second law only if there were no external forces acting upon them, which is not the case.

That being said, gravity itself is not an energy source. Objects in a gravitational field possess gravitational potential energy. But that energy does not originate in the gravitational field. To illustrate, say a mass, m, sits on the surface of the earth. With respect to that surface it has zero gravitational potential energy and zero kinetic energy. If you elevate the mass to a height h above the earth it gains gravitational potential energy $PE=mgh$. But that energy had to come from some external agent that did work $w= Fd=mgh$ to get it there. If the mass is subsequently released or otherwise allowed to fall it will lose its gravitational potential energy and have all kinetic energy just prior to impact where $KE=1/2mv^2=mgh$ (neglecting air resistance). The source of that kinetic energy is not gravity, but the external agent that supplied work to give it its potential energy in the first place.

Regarding the container of gas sitting on the ground, the gas molecules at the top of the container possess more gravitational potential energy than those at the bottom. These molecules got there because they individually had higher kinetic energy that could be converted into gravitational potential energy over some period of time than those at the bottom. Albeit there are fewer of those at the top (less density).

Regarding the question of the partitioned container of gas “floating in space” (and thus presumably not subject to any gravitational forces other than those between the molecules themselves) consider the following:

A real gas would be subject to intermolecular forces electrostatic in nature. An example is Van der Waal forces. On a molecular level the electrostatic forces, which would be many orders of magnitude greater than the gravitational forces between them, would, I think, keep the distribution of molecules uniform in each chamber.

Hope this helps.

• Thank you for the elaborate answer, I did not consider the potential/kinetic energy aspect. When you say " like those higher in the atmosphere, got there because they individually had higher kinetic energy" does this mean the temperature of the gas is higher on top - because higher kinetic energy means higher velocity and higher velocity of molecules is associated with higher temperature? – Csaba Garay Jul 26 '18 at 14:44
• No, the temperature would not be higher. The key word is that the molecules had (past tense) higher vertical component of KE at the bottom. But as they rise they give up KE in exchange for gravitational PE. Picture a room full of bouncing balls making elastic collisions with the floor. The balls that come off the floor with higher vertical component of KE will bounce higher. At the top of the bounce they have no KE (its all PE). They then fall and gain KE. A snap shot of the room will show fewer balls at the top than bottom. But the KE of each will vary with height being max at the bottom. – Bob D Jul 28 '18 at 0:25
• The situation with high elevations in the atmosphere is more complex, so I edited that reference out of the answer. – Bob D Jul 28 '18 at 0:27

A typical problem with thermodynamics is the misunderstanding of its meaning.

Thermodynamics describes the behavior of energy in a system and its subsystems. It is pretty abstract and subjective.

• Subjective, because it deals only with one closed system, e.g. the container (real systems are mostly open, and have no boundaries, think on a tree, a cow or the sea) and only one level of subsystem: particles (real subsystems can process energy for multiple levels, e.g. a particle can be split into atoms, ergo allowing a larger entropy on the same system).
• Abstract, because it simplifies energy to be manifested in elementary forms: heat, pressure, etc. In reality, energy has multiple forms, not just those addressed by thermodynamics. For example, electromagnetic, atomic, gravitational, chemical, etc. If you need to include chemical energy in your thermodynamic assessment of a system, see chemical thermodynamics, and so on.

So, under such constraints, thermodynamics says: a) energy conserves (even if internal gravitational energy is present) b) energy tends to disperse within the subsystems of a system (including gravitational). This means that all the subsystems will tend to have the same energy. That is the second law's significance.

If you think it, the first law describes the SYSTEM, the second law describes the SUBSYSTEM, the zeroth law describes our subjectivity (just think on it: temperature is just a feeling, the zeroth law formalizes it), and the third law just describes the limit of the second law. I would personally state that systems are fractals: they are made by systems and they contain systems, infinitely. But not for thermodynamics, there are only two systems in thermodynamics, the container and the particle; the third law defines the limits of the subsystem (where no more subsystems are possible), by determining the point where entropy is zero; the zeroth law defines the limits of the system (where no more supra-systems exist, by defining what is our understanding of energy (the definition of temperature), in fact, some cientists have proposed to express temperature in joules.

When you state that particles tend to be localized in a zone of the container, you are implying a subjective interpretation of the behavior of the molecules. Within classical thermodynamics, molecules will move and distribute homogeneously (you can understand that as disorder, and I can interpret that as order: order is a subjective appreciation). But in your thermo-gravitational-dynamics, molecules might fall down (implying that they are not perfectly elastic, as classical thermodynamics do). Perhaps they will. So you are concluding that the second law is failing and entropy decreases in a closed system, because we can clearly see that molecules tend to order.

But that is wrong! The second law is not about disorder! It just states that energy will disperse across the subsystems of the system. Such is a common misunderstanding. Entropy is not disorder, but moreover energy dispersal (do not forget: there are only two types of systems in thermodynamics: containers and particles; entropy means energy dispersal within particles; just that). So even in the case that particles group inside the container, entropy reaches its maximum (within the SUBSYSTEMS) , spontaneously, energy conserves (within the SYSTEM), and order or disorder are subjective appreciations (within our OPINIONS).

You are missing an important point of the 2nd law. It implies that the gas will be evenly spread out when there are no outside influences.

In your descriptive case, when the box of gas is on the surface of the Earth, it is not an isolated system. Gravity (from Earth) is an outside force acting on it.

• That was exactly my point that if you have a box with gas evenly spread out it would mean there are no outside influences. But because observation on Earth is that gas in a container have increasing density towards one side of the container there must ben an outside influence. My understanding was that the outside influence is always due to outside energy hence I drew the conclusion that if gravity is the cause then gravity must be energy. In the second part one container with a wall is considered - so it is a closed system - and due to it's own gravity molecules must pull towards the wall. – Csaba Garay Jul 24 '18 at 8:29
• This thread also seems to be relevant: physics.stackexchange.com/questions/286915/… – Csaba Garay Jul 24 '18 at 13:51