Motion System Design

A rip in time makes nine

From the erosion of a grain of sand off a cliff to the unbounded expansion of the Universe, Nature tends towards disorder. This tendency has a name — entropy. The phenomenon has specific scientific meaning, but in everyday popular culture, is described succinctly and wittily by the infamous Murphy's Law — What can go wrong, will go wrong.

Call me irreversible

Shattering a glass, scrambling an egg, sending an unfortunate reply-all email — what is it about these actions that makes them impossible to reverse? Well, that's complicated; the orderly reassembly of atoms or restoring of situations breaks a few rules of our universe, not the least of which have to do with directionality of space-time.

Suffice it to say that irreversible events are in effectively closed systems, and it's a law of physics (the Second Law of Thermodynamics, to be exact) that entropy, sometimes also called the Arrow of Time, always increases in such situations. In theory, reversible processes do exist — for example, squeezing air from one end of a balloon to another — but in reality, even these create friction and other nonreversible results.

What's more, the entropy of two joined systems is greater than the pair's two entropies if they remain separated — as the removal of a boundary to allow mixing makes for a less organized situation.

Entropy and black holes

Mexican-born Israeli Jacob Beckenstein proposed in 1972 that even black holes obey the Second Law of Thermodynamics, and have a definable amount of entropy. This implies that black holes also have a temperature, and emit the associated radiation and particles — something that Stephen Hawking reluctantly confirmed a year later. Today it is generally accepted that a black hole's event-horizon area is a measure of its entropy.

Tomato, tomaaato

Just as light can be defined as a particle or as a wave, so too can entropy be scientifically described in two different ways. The first way is in terms of heat — a view developed by Frenchman Nicolas Léonard Sadi Carnot in 1824.

Assume that we have a two-chambered insulated tank; ideal gas fills one half. If we remove the barrier between the two chambers, our ideal gas will expand to fill both evenly. The increase in entropy for an isothermal process is:

Measured in Joules per Kelvin, this entropy change does not need to be expressed as the integral, as it is equal to that of a reversible process with the same initial and final states.

Fan of the flames: Sadi Carnot wrote his short book, Reflections on the Motive Power of Fire, in 1824. It details how motion can be generated from the “fall” of heat from one object to another colder body. It also first outlined the Second Law of Thermodynamics.

Murphy's Law:Correlates and functions

If left alone, things tend to go from bad to worse. • If a series of events can go wrong, they will do so in the worst possible sequence. • Nothing is as easy at it looks. • If everything seems to be going well, you have obviously overlooked something.

Tune in to next month's issue of Motion System Design, when we'll explore the second way to define entropy — with statistics.

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