How do we or can we prove ORDER/DISORDER

[TheYoungFella]

I recently quoted the various laws of thermodynamics to someone recently and they replied that we could never prove that unless the universe was ordered.

Obviously this would increase it's disorder and negate the measurement so how do we or can we prove entropy at all.

 

[TheYoungFella]

I found this post on the very subject in Yahoo Answers

Question---- Entrophy can we prove it?
If the only way to measure something is to increase it's disorder do we really have any proof for the Laws of Thermodynamics


Answer----The principles of thermodynamics, as they are currently presented, are axyomatized. They are based on years of experience on the labs (well before the 20th century) and are gathered as a series of propositions which have been put to the test time and again. So that makes us fairly confident that they are reasonable; but not completely sure that they are correct. By themselves, they are consistent; but although that is "necessary", it is not sufficient, so they've been proven time and again in the lab. However, by the same token, that makes us more suspicious about new things (ideas) that collide with predictions from thermodynamics.

Nevertheless, the thermodynamical concept of entropy has no mechanical equivalent, and that makes it difficult to explain in everyday terms. The same math is used in information theory, so that gives another way to explain entropy (in absolute value) in terms of the "level of disorder" of a system. However, physical systems don't deal with entropy in absolute values. Thermodynamics deals with PROCESSES, which involve exchanges of work and of heat (in the case relevant for entropy). For example, we don't say in thermodynamics: "System X has entropy S" but "System X has suffered a variation of entropy dS due to the exchange of heat dQ through its frontier". The thing is, if we put in entropy (and the rest of thermodynamics) it gives out the correct answers -- what is predicted comes out as the same as measured in the lab. That's our measure of confidence in it. We don't exactly "prove" the laws of thermodynamics.

 

[rkmurtyp]

I do not know how you stated (or quoted) the laws of thermodynamics (TD, for short), for the others to counter stating that 'we could never prove that unless the universe was ordered'.

TD is really simple, unfortunately it is taught and understood in a complicated way, especially with the advent of statistical thermodynamics.

The issue before us concerns the second law of TD, the concept of entropy and its relation to order/disorder and the proof thereof.

The laws of TD cannot be proved.

In geometry, a point has no dimensions, a line has one dimension.The points we show on a paper, the lines we draw on a paper, are not really true points or lines - can we ask for a proof in this case? Can we prove a point has no dimensions or that a line has no width and thickness? Since the axioms appeal to our senses, that is, since we can feel their truth, we don't ask for a proof.

Similarly, the observation that when two bodies at different temperatures are brought into thermal contact, the one which was hot to start with becomes colder and the one which was cold to start with becomes hotter, and the two come to the same temperature eventually appeals to our senses. Though we did not define many terms used here (such as temperature, hot, cold, hotter colder etc.) we understand what is being stated. This fact of natural phenomenon is known for centuries and we believe is valid for ever.

This fact is stated in more precise terms in the form of a postulate that we now call the second law of TD. We give Fermi's statement: A transformation whose only final result is to transfer heat from a body at a given temperature to a body at a higher temperature is impossible. Do we need a proof for this statement? Well, if you insist, there is no proof!

The concept of entropy is generated from this statement, in classical TD.

However, statistical thermodynamics tries to explain entropy in terms or order/disoder. Here the second law is a theory-based second law and is derived from a predefined concept of entropy. Hence questions such as the one you faced arise and are discussed endlessly.

In classical TD there is lesser scope for such questions to arise.

 

[TheYoungFella]

I got the sense it was a well prepared answer from a person on a mission to prove Gods existence. He was quite clever he knew how to tangle me up in a more philosophical bent ie i can't 100% prove X so why is it a LAW etc etc.

basically trying to get me to say we using faith in engineering and science

 

[Studiot]

You have certainly stated a good deal of text.

Unfortunately I can't agree with some fundamental points.

In particular the statement that entropy has "no mechanical equivalent" is plain rubbish.
But then what do you expect from Yahoo?

Entropy was introduced as that property which yields the mechanical work done when combined with temperature (in a T-S diagram) in the same way pressure is that function which yields mechanical work done when combined with volume ( in a P-V diagram). In both cases it is the area enclosed by some indicated path traversed on the diagram.

As regards proving order or disorder - the question is meaningless.

If a system can exist in more than one state we select any single one of these and call it 'order'. Every other state is, by definition, disorder.
Having done this we can apply the rules of probability to the list of states of our system.