Why does the motion of a gas never stop?

Question

It is said that if a container is filled with gas, the gas molecules perform random motion in every direction.

Pressure should be exerted on the walls of the container due to the collision of gas molecules with the walls of the container.

My Question:

1. As the molecules of the gas collide with the container do they lose some energy (kinetic)? - as no collision is perfectly elastic in nature.

2. If they lose energy, then they should stop moving after a period of time and also the pressure on the walls of the container should become zero.

---(For real gases not the ideal one)

Answer 1

The molecules which make up the walls of the container are also undergoing random thermal motion.

If you put a hot gas into a cold container, the gas molecules will on average lose energy during their random collisions. But if you put cold gas into a hot container, the gas molecules will on average gain energy during collisions. When the average energy exchange during a collision is zero, we say that the gas and the container have the same temperature.

Answer 2

It might be worth pointing out that at molecular level, perfectly elastic collisions can happen. Take for example two protons. When they are stationary & at distance $r$ apart, their kinetic energy is $0$ and potential energy is $kq^2/r^2$. If they were released, then at $\infty$ their potential energy would be $0$ and their kinetic energy (by conservation of energy) $kq^2/r^2$. In other words, you can collide two protons with KE $kq^2/r^2$ and still get two protons with KE $kq^2/r^2$.

Indeed, the kinetic theory of gases treats collisions between molecules as perfectly elastic.

Answer 3

Damping can add energy.

The more damping there is the more the kinetic (or potential) energy of, say, a swinging pendulum is brought toward the thermal equilibrium energy. The equilibrium energy is a random variable with distribution E ~ exp$(-x/(k_b T))$ among the allowed energy levels. The higher the damping the faster this maximum-entropy state is achieved but the end result is the same.

The kinetic energy of a bouncing superball is far higher than $k_b$T = 4.14e-21J. Friction and damping dissipate this energy as heat.

Each gas molecule in a jar of gas, at constant temperature, is already at thermal equilibrium. Damping randomly removes or adds energy to each molecule with no net effect.

If, for whatever reason, motion is slowed down below the thermal equilibrium level damping will add energy. This is the case for the LIGO mirrors which are held extremely still. To reduce noise they hang them by special fused quartz fibers with very low damping. They also actively remove energy.

Gas-gas collisions between monotonic gases at ordinary temperatures are almost perfectly elastic. It is very unlikely for energy to be lost via emission of photon(s).

Gas-solid collisions, however, are mostly inelastic with very high damping. In a high vacuum hot gold can be evaporated and condense, atom by atom, onto a cool surface. The atoms immediately lose their energy and don't bounce off.

Answer 4

As the molecules of the gas collide with the container do they lose some energy (kinetic)? - as no collision is perfectly elastic in nature.

In a microscopic system collisions are elastic. Energy is always conserved. On a macroscopic scale, energy is conserved but according to our daily experience it might seem like it's not. Cars stop rolling without gas, balls stop bouncing, paper planes always land, etc. The kinetic energy leaks to other kinds of energy, like heat and sound and our minds interpret this as energy that is lost.

On a microscopic scale however, there is nowhere for the energy to go. Heat and sound are kinetic energy on a micro scale. The reason the molecules don't slow down is because together they hold some amount of energy and the molecoles cannot shed this energy without leaking it to somewhere else. The molecules might lose or gain energy by colliding with other particles, but the average energy stays the same because of conservation of energy. In fact, temperature is often defined as the average energy.

Answer 5

As the molecules of the gas collide with the container do they lose some energy (kinetic)? - as no collision is perfectly elastic in nature.

They can, but not because of elasticity of collision. Elasticity and the associated coefficient of restitution is a statistical quantity that only applies to a large amount of molecules, not to individual molecules. On molecule level, collisions do not result in energy loss but just transfer between different forms and modes of energy.

For example, a collision can convert energy from linear movement to rotational movement or to molecular vibration. But then the next collision might convert it back to linear again.

The gas molecules will lose energy when colliding with the walls on one condition: that the walls are colder than the gas. So if you put gas inside a cool box, the gas cools down and the molecules slow down. This happens because the wall molecules, on average, receive more energy in collisions than they give back.

This method is used in practice in every fridge, and at very low temperatures buffer gas cooling is used where the "walls" are actually cold helium gas.

If they lose energy, then they should stop moving after a period of time and also the pressure on the walls of the container should become zero.

Theoretically at absolute zero temperature, the molecules would eventually lose all of their kinetic energy. But the slower the molecules move, the less often they hit the walls, and therefore they can't lose the last bit of energy.

Answer 6

Why does the motion of a gas never stop?

It does stop, eventually. Well almost. Over an infinite period of time, the motion will approach zero. Consider a closed vessel in space containing a gas under pressure at room temperature. Since there is no such thing as a perfect insulator, the walls of the container will lose thermal energy to space and tend towards thermal equilibrium with the CMB temperature. When the gas molecules collide with the cooled vessel walls, they will transfer energy to the walls, which in turn radiate energy into space. This will reduce the average kinetic energy of the gas molecules and, therefore, reduce the temperature (and pressure) of the gas. Over eons of time, the CMB is also cooling and tending towards zero Kelvin as the universe approaches heat death due to the laws of entropy. The pressure of the gas will tend to zero as the age of the universe tends to infinity.

Just to elaborate a little, when individual gas atoms collide with each other, the collisions can be perfectly elastic as individual atoms do not have a temperature. However, when the atoms collide with molecules in the walls of the vessel, the molecules have intermolecular forces with other molecules in the walls, and kinetic energy from the colliding atom disperses in all directions inside the walls of the vessel, and eventually, the heat energy is dispersed into the vacuum of space.

When the universe eventually dies a heat death, there will not be anything with a temperature or pressure left, including our pressure vessel, which will die along with the rest of the universe. However, one of the laws of thermodynamics is that absolute zero can never be attained, so as the age of the universe tends towards infinity, the temperature of the universe (and the pressure of the vessel) will asymptotically approach zero.

If we were to put the pressure vessel in a room with fixed air temperature and ignore the heat death, no energy would be able to leave the vessel, and it would effectively act like a perfectly insulated vessel. When gas atoms collide with the walls, the molecules in the walls can gain some thermal energy. Since this additional energy in the walls cannot be exported to the room, other atoms will gain energy from the thermal oscillations of the wall molecules they collide with, and so the average kinetic energy of the gas atoms as a whole will remain constant. This means that the temperature and pressure of the gas in the vessel will remain constant, so we can consider the collisions between the atoms and the walls to be perfectly elastic as a collective property in this case.

Answer 7

The real answer is that entropy always increases in a system by fundamental laws of thermodynamics. As entropy decreases within the container, it increases in the container itself and/or in the universe surrounding the container.

In a real physical system, your container is not as isolated as it is in a textbook. However, even if it were in interstellar space, at 3 Kelvin, and even if kinetic energies of various degrees of freedom were to transfer from the trapped "real" gas to the container itself and eventually escape from the container to emit blackbody radiation into interstellar space, eventually equilibrium would be achieved at 3 Kelvin and the associated pressure within and without the container would remain more or less constant with negligible fluctuations.

There would always be at least a little kinetic energy remaining. An ideal gas would not behave much differently from what you call a "real" gas. Believe it or not, physicists know what they are doing when they make these sorts of approximations.

Answer 8

Gas molecules collide not only with the container walls but also frequently with one another. The energy exchange during these collisions depends on the temperature of the walls. If the walls are warmer than the gas, molecules can gain energy; if cooler, they lose energy.

While gas molecules may slow down due to energy redistribution, they never stop moving entirely. Even in a solid, molecular motion continues until the temperature drops to absolute zero—a state that cannot be physically reached.

Answer 9

The problem is that, with real gases, the internal area of the container is not a closed system, and the container walls themselves are neither fully stationary nor opaque.

What I mean by "not closed" is that there remains a universe of influences outside the container walls that can continue to permeate to the inside of the container and perturb the gases within.

And what I mean by "not opaque" is that the container wall presents much like a string vest or swiss cheese as far as excluding the passage of influences is concerned.

Even where the container is sufficient to contain the gas molecules themselves and prevent ingress of any gas molecules from outside, there are many other things currently conceived as particles that it does not stop the passage.

Moreover, what I mean by "not stationary" is that the walls of the container, because they are not infinitely rigid, are capable of mediating energy directly between the internal and external areas, in the style of Newton's cradle, without any particulate or molecular matter crossing the boundary of the wall and without permanent deformation of the wall.

The larger implied question of why the universe doesn't settle into a stationary state is a cosmological one, but there's really no evidence that settlement looks like a stationary state rather than a circular progression.

That is, when a physical system is left to settle, it mostly appears it settles into a recurring pattern of activity, not into a cessation of activity - the principle that explains this is called "energy conservation", which states that whilst specific forms of physical process can sustain "losses" which abate their recurrence when not further driven, there is no overall loss when all physical processes in the system are accounted for, only a transformation of activity from one process to another.

Answer 10

It actually stops. https://en.wikipedia.org/wiki/Heat_death_of_the_universe But not anywhere close to our lifetimes.

Probability of emitting a photon from collisions at room temperature is so small, that energy has nowhere to go.