Why do things decay?

I've talked about this before when I discussed entropy, but I thought it would be interesting to explore the physics of it more thoroughly.

Entropy is a thermodynamic variable usually designated with 'S' and it can be thought of as measure of disorder in a thermodynamic system. The second law of thermodynamics says that entropy can never decrease in a closed or isolated system. In other words, thermodynamic systems run down without applying new energy to them. Thus a system that is not isolated could decrease in entropy if it increases the entropy of its environment. Energy must be added from the outside.
Most entropy changes involve heat transfer because most engines run on heat energy being converted to mechanical energy. This idea was spawned out of the industrial revolution in which steam was the main power source for trains and manufacturing equipment (think Steampunk here). The only time that entropy can be conserved (not changed) is in a reversible system, which is theoretical. All practical power systems are irreversible and cannot conserve entropy. Thus, in the real world, entropy increases.

Think of it this way. You burn fuel to power your automobile. The fuel is combusted and converted to mechanical energy to drive your car down the road. Because of friction and the fact that fuel combustion is not completely efficient, some heat is lost. This is how the entropy is increased. When you burn fuel, hydrocarbon molecules are oxidized into carbon dioxide and water. In order to make hydrocarbons from this carbon dioxide and water, you would need a heck of a lot of energy. Thus the ordered molecules of the hydrocarbon are converted by combustion into less ordered molecules of carbon dioxide and water. Order is converted to disorder. That conversion involves an entropy increase. Entropy (and the second law of thermodynamics) is the reason you must keep putting gasoline (petrol) in your automobile. Sorry!

The above is why it's impossible to create a perpetual motion machine. Friction will eventually make it stop. To keep all machines going, energy must be constantly added, thus causing an entropy increase.

Entropy does have units, and for thermodynamic systems they are one calorie per Kelvin degree per mole or 4.184 joules per Kelvin degree per mole. From this it's obvious that entropy change is dependent on the temperature of a system and the amount of stuff being combusted. A mole is an Avogadro's number (6 to 10^23) of atoms or molecules of a substance.

Entropy can be explained by using statistics. Let's say you have two atoms of hydrogen in a confined space V1. The probability of finding one atom of hydrogen in V1 is 1. Let's say that half the volume of the space is V2. The probability of finding one atom in V2 is 1/2. Now the probability of finding two atoms in V2 is 1/2 X 1/2 or 1/4. Finding 4 atoms in V2 would be 1/16. If we started with V2 and expanded to V1, the atoms would distribute evenly. So we could say that the entropy S is equal to k (a proportionality constant) times ln W, where ln is the natural log and W is the probability. This defines the spontaneous change from the lowest to highest state of probability. This relies on the idea that as we increase the number of molecules the entropy increases proportionally.

This is only for one system. We need to calculate the change in entropy for a transfer from one system to a second system. This change would be Delta(S) = S2 - S1 = k ln (W2/W1).  If we assume that this is a system of expanding gas molecules and doing some math we end up with Delta(S) = N k ln (W2/W1) where N is the number of molecules, k is the proportionality constant, W2 is the probability of system 2 and W1 is the probability of system 1.
Using the Boltzmann constant (k = R/N where R is the gas constant and N is Avogadro's number) and some more math we end up with Delta(S) = n R ln (V2/V1). This means that the change in entropy Delta(S) is equal to the number of moles, n, times the gas constant, R, times the natural log, ln, of Volume2 (V2) divided by Volume1(V1). The gas constant R is 8.3145 Joules per mole per Kelvin degree. This comes from the gas equation PV=nRT. All of this comes from a statistical method of calculating entropy. Easy isn't' it? I can imagine you laughing here!

Entropy is why things decay, why stuff wears out, and why energy is lost forever. There is only so much energy in our universe that was created at the time of the Big Bang. Energy is slowly being consumed (order converted to disorder) and will eventually (trillions of years) run out. Thus, you could blame entropy for the demise of the universe. Entropy is the reason that we age and die. It's responsible for the eventual demise of our sun and the entire universe.

Since the second law of thermodynamics says that entropy cannot decrease, entropy becomes a clock of sorts. And since it always increases, it's the reason that time only goes forward. In order to go back in time, one must violate the second law of thermodynamics. This is why they call it the arrow of time and it only goes forward.

That's what entropy is in a nutshell.

Thanks for reading.