why does the distribution of peas in a pan of swirling water restore itself even as I spooned them out in batches (I.e. where I spooned peas out the area in water did not stay empty).
In: 4
What you have observed was actually a really interesting demonstration of entropy. When you have 2 areas of unequal energy, the energy will flow from the high side to the low side until the energy is equal.
In this case that energy is the peas being jostled around by the water. They are bouncing of of each other. There is a balance and each individual pea ends up running into another after a little bit. Now you take a big spoonful out and suddenly there’s this big gap where the peas can move freely into. So they do. Bit by bit peas get randomly jostled into the gap. Once the gap is filled then then every pea has an equal chance of bouncing off another one.
What you have observed was actually a really interesting demonstration of entropy. When you have 2 areas of unequal energy, the energy will flow from the high side to the low side until the energy is equal.
In this case that energy is the peas being jostled around by the water. They are bouncing of of each other. There is a balance and each individual pea ends up running into another after a little bit. Now you take a big spoonful out and suddenly there’s this big gap where the peas can move freely into. So they do. Bit by bit peas get randomly jostled into the gap. Once the gap is filled then then every pea has an equal chance of bouncing off another one.
Statistics!
Let’s look at the most extreme example, where one area is *full* of peas and the other area has none.
A pea may wander into the empty area from the full area, but there is no chance of a pea wandering from the empty area to the full area (since there are none there).
The same logic applies if only one pea is in the empty space. The odds of that one pea wandering into the more full side are pretty small compared to the odds of any of those peas wandering to the empty side, because there’s more of them.
Statistics!
Let’s look at the most extreme example, where one area is *full* of peas and the other area has none.
A pea may wander into the empty area from the full area, but there is no chance of a pea wandering from the empty area to the full area (since there are none there).
The same logic applies if only one pea is in the empty space. The odds of that one pea wandering into the more full side are pretty small compared to the odds of any of those peas wandering to the empty side, because there’s more of them.
This is an interesting observation. It’s a demonstration of how processes that are individually quite random (such as the random motions of a pea swirling and tumbling around in turbulent water) on the whole result in the Second Law of Thermodynamics which is a quite predictable result.
That is, a system that contains a large number of individually random events and processes, will tend towards a state of greater randomness and more uniform distribution of matter and energy, rather than one of greater order or seperation.
More specifically. If you have a single pea swirling around in a pot, then the odds that it would travel into an area where you’d previously ladled, is pretty low although given enough stirring and time it might.
However if you have ten peas, then odds are pretty good that at least one will travel into such an area quickly. If you have 1000 peas, then the odds are almost certain that a few will immediately migrate into the space where you’d just scooped some of them out. In fact the odds that none of the peas will travel into that space are trivially, ridiculously low. Moreover such random motions will, with 1000 peas, quickly act to make the distribution relatively uniformly.
This is an interesting observation. It’s a demonstration of how processes that are individually quite random (such as the random motions of a pea swirling and tumbling around in turbulent water) on the whole result in the Second Law of Thermodynamics which is a quite predictable result.
That is, a system that contains a large number of individually random events and processes, will tend towards a state of greater randomness and more uniform distribution of matter and energy, rather than one of greater order or seperation.
More specifically. If you have a single pea swirling around in a pot, then the odds that it would travel into an area where you’d previously ladled, is pretty low although given enough stirring and time it might.
However if you have ten peas, then odds are pretty good that at least one will travel into such an area quickly. If you have 1000 peas, then the odds are almost certain that a few will immediately migrate into the space where you’d just scooped some of them out. In fact the odds that none of the peas will travel into that space are trivially, ridiculously low. Moreover such random motions will, with 1000 peas, quickly act to make the distribution relatively uniformly.
Latest Answers