What is Entropy?
"Entropy is a measure of randomness and entropy of the universe increases." I studied this few years back without understanding. Whenever I imagine to explain this sentence, I cannot come up with examples.Can someone explain this term in plain english?
The famous example is dropping a tea-cup.
Initially the molecules in the clay are ordered in the shape of a cup. When you drop it and it
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breaks the molecules are in a more random order. If you pick up all the pieces and shake them you can be fairly certain that they will not re-form into the shape of a cup.
It's got something to do with the direction of time, you can tell which way time is moving by the increase in entropy.
The teacup example is always a good one. There is a law of physics which says that entropy
always increases. What this means in practice is that, left to its own devices, everything
decays.
It's also related to the total amount of energy in the universe. The total amount of energy
can never decrease (where would it go?). The thing is that objects with low entropy (ie they
are highly 'organised', like an unbroken teacup) have more energy than those which aren't
(the broken teacup) because it takes energy to keep them that way.
My desk is really untidy, with things strewn at random on it, so it's got a very high entropy.
If I were to tidy it up I would be expending energy by doing so, so the total amount of energy
in the universe would decrease. However, I would be decreasing the entropy of the desk by
tidying it up, and if you measured the energy in the desk (held because of it's low entropy)
you would find that it exactly cancels out the energy I've spent in tidying it, so the total
energy of the universe has actually stayed the same.
The fact that entropy always increases with time means that an unbroken teacup will smash
when dropped (it's entropy will increase) but a smashed one will not reform itself when dropped
(which would mean an increase in entropy).
In classical thermodynamics, energy is constant and entropy never decreases. But entropy may
stay constant. Entropy is a really hard concept to understand. It is not a "thing" such as mass
or lenght which can be measured more directly. The definition of entropy is:
dS = dQ / T
Where S is the entropy, Q is the energy (heat) and T is the teperatue.
The second law of thermodynamics state that entropy must either increase or stay constant
on every fenomena. If it stays constant, it means that the process is reversible.
Entropy is a "thing" that you calculate, but can't measure directly, to tell you if a process
is reversible or not.
If you are converting a type of energy A to another type B and the entropy increases in the
process, then you can't convert it ALL back from B to A. If the entropy remains constant,
then you can convert A to B and B to A with no loss of energy.
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For example, a simple IDEAL pendulum. It converts gravitational energy into kinetic energy and vice versa, with no loss. Its entropy remais constant.
A engine of a car converts chemical energy from the gas to mechanical energy. But the entropy increases in the process, so you can't convert all the mechanical energy back into the chemical energy stored in the gas. You lost some energy in the form of heat and sound and other kinds of energy.
Entropy is often called "the arrow of time". It shows us in which direction the time is flowing. If we take a physical non-reversible process and reverse the time, entropy would decrease. And according to thermodynamics this is impossible. So we know in which direction the time is flowing.
Let's take some examples on time reversal. If you watch a tape of a pendulum moving, you can't tell if the tape is moving forward or backwards. The movement of the pendulum is the same if you hit "fast forward" or "rewind". So, when you reverse the time, the process suffers no change. That means its entropy is constant and the process is reversible.
If you watch a film of a bomb exploding, or an egg falling to the ground, or a tea cup braking, you can easily tell if the tape is moving forward or backwards. That is possible because in this process the entropy is changing, and the reversal of time is not possible. You will never see a broken egg becoming whole again, as in the reversed tape.
Another great example my teacher gave me once is about life on earth. People think that life on earth is possible because the sun is giving energy to it. But the truth is that the sun is giving "negative entropy" to the earth.
If the sun was really giving energy to the earth, then the earth would heat up and up and up, with no limit. The same amount of energy the earth receivers from the sun it gives back to the rest of the universe. So the temperature of the earth remains approximately the same.
Well, the amount of energy the sun gives to earth is the same the earth gives back to the universe, lets call it Q. So the entropy the sun is giving to the earth is Q/Ts (Ts is temperature of the sun) and the entropy earth is giving to the universe is Q/Te (Te is temperatue of the earth). Since Ts > Te, then Q/Te > Q/Ts.
So, the earth is receiving Q/Ts from the sun and is giving away Q/Te to the rest of the universe. So the change of entropy on the earth is Q/Ts - Q/Te < 0. So entropy on earth is decreasing.
Since life forms are more organized than a soup of atoms and molecules, to have life a planet must organize itself, ie, must decrease its entropy. That what is happening to the earth due to the sun. The sun is decreasing the entropy on earth.
Now you might ask "but how can entropy decrese on earth if it must always increase or remain constant?" The answer is that the entropy of the whole system (sun + earth + universe) is increasing. The entropy of parts of a system may decrese, since the total entropy of the system either increases or remains constant.
From memory there are certain circumstances under which entropy can actually decrease.
As far as I remember this result comes from (what I was taught as) the orginal derivation
of entropy. This examined the case of a chamber with a partition. One section had a gas
and the other section did not. As time goes on we'd expect the gas to cover the whole chamber.
However, due to probabilities and given an infinite amount of time, it is possible that the
gas may realign itself to it's original configuration. This is so incredibly unlikely
that realistically it will never happen - but given an infinite amount of time, it WILL.
I appreciate that we're dealing with something incredibly unlikely, particularly when we
deal with larger systems, but it's still an important point. If people dispute my recollection
of things, I'll try to find the book that taught this fact. I have a feeling Roger Penrose's
"The Emperors New Mind" tackles the subject quite well...
What is the difference between an event that never happens and a event that takes forever to happen?
This reminds me of a discussion about if it were possible for one person to win the lottery. On one hand, some people alredy won, so it is possible. But it is so unlikely (1 chance in millions) that if this was a physical event it would be considered an impossible event.
Sometimes in physics you consider impossible an event that has an extremely low probability to happen. If you have a electron in canada, it is "possible" to measure its position as beeing in japan, but the chance is so extremely low that you can say that it is impossible for a electron in canada to be measured in japan.
You've precisely countered your argument. While "a" person may win the lottery, an individual may not. We don't categorically know how big the universe is. We don't know if there is a "multiverse". So considering such events is theoretically productive. There was a theory that our viewable universe was in fact one of these aberrations. Of course, it can never be proven (which means it can't be called a theory?).
I'm not trying to be annoyingly pedantic - rather just looking for completeness. You can't do any statistics unless your probabilities add up to 1. The normal curve doesn't exist without those really unlikely probabilities. Nor does integration. The only reason I mentioned this little element was because it's slightly counter intuitive and often left out. It only makes up a tiny part of what entropy is all about!
"You've precisely countered your argument. While "a" person may win the lottery, an individual may not."
Let's say that the lottery has 50 million possible combination of numbers. If 100 million people play it, there is a high probability that one or more persons win it. But the probability that you win it is very very low.
The probability of ONE specific person winning the lottery is so low that it can be considered impossible. But the probability of ANY non-specific person winning the lottery can be very close to one.
Making a calculus analogy, the probability of one person winning is the differential. The probability of any person winning is an integral. A differential has a value so small that alone it can be considered zero, but when you integrate the differentials, it may have a big value.
Contributors : lexxwern, RobinD, riccohb, acerola, gd2000, prashant_n_mhatre
