What is the relationship between thermodynamics and classical mechanics?

[springwave]

I have just completed an intermediate course in classical mechanics. I am very comfortable with the subject, and I really enjoy solving the problems. I just love the idea, of describing everything in nature in terms of forces and their resulting accelerations.

Now, I have started an introductory course in thermodynamics, and I am finding it very difficult to adjust to some of the basic ideas. I am unable to understand the need for thermodynamics as a separate entity in physics.

For example consider, the heating of an ideal gas in a closed container. We know the temperature of the gas will increase. This is explained by thermodynamics as:

"During the process of heating, heat is supplied to the container, and is transferred to the ideal gas inside. This heat is completely utilized in increasing the internal energy of the gas and hence it's temperature"

We could also explain like this :

"The flame used to heat the box contains many air particles moving around at very high speeds. When the flame comes in contact with the box, the molecules of air collides with the surface of the box setting the molecules of the box into motion. This motion is slowly transmitted to the inner surface of the box through internal collisions. Due to this motion, gas molecules which collide with the inner surface of the box gain more velocity, and hence their average kinetic energy increases, and thus the temperature of the gas"

Aren't these two explanations, exactly equivalent to each other? The second is just the microscopic explanation right?

If every thermodynamic phenomenon could be explained in terms of collisions, and changes in kinetic energies of atoms, then why is there a need for a new subject called thermodynamics.

What are the thermodynamic phenomena that classical mechanics (simple collisions) cannot explain?(not considering any quantum effects) Can thermodynamics be thought of as a subset of classical mechanics?

Why can't heat be described simply as normal kinetic energy? Why do we have to draw a line between kinetic energy on the macroscopic level, and that on the microscopic level

 

[K^2]

These are equivalent descriptions. Now, using your knowledge of mechanics show that if I get two objects in contact with each other, their temperatures will equalize.

That's why you need thermodynamics.

 

[Bandersnatch]

It would be impossible to solve any equation describing a macroscopic process like heating using only classical mechanics. Even as simple problem as three bodies interacting with each other gravitationally only, cannot be solved apart from certain special cases.
Imagine 10²² particles(roughly that many atoms in 1g of whatever) exchanging momentum and energy, interacting electromagnetically and gravitationally, losing and gaining electrons, radiating energy and whatnot, many times each second.
There's no way to solve such complicated equations, and the only viable, numerical, approach would take ages to crunch the numbers even for the fastest computers we've got.

It's much simplier to treat the thermodynamic processes statistically.

 

[ModusPwnd]

Thermodynamics is a "higher level" theory, that is - it doesn't use "fundamental" postulates. It uses observed phenomenon as postulates and then you get your theorems from there. You can also use the "fundamental" postulates/axioms from classical mechanics and statistics to derive the same theorems. This is of course statistical mechanics and it bridges thermodynamics with classical mechanics.

Either approach may be more or less useful depending on what you are doing and each approach is still useful to teach and learn. Stat. Mech is a more "fundamental" theory in that it satisfies our presumptions of a downward causality and connection of higher level macroscopic physical laws/models of complex systems to microscopic physical laws/models of simple systems. But thermo also yields you results and intuition by consideration of macroscopic behaviors alone.

 

[dydxforsn]

You could indeed prove everything, that's what you do in a course called statistical mechanics (you're going to enjoy it, one of the great fields in physics). Of course you don't ever add up all of the data for each particle individually, but a combination of first principles from mechanics and statistical methods is what takes place when proving ideas of temperature and other thermodynamic concepts from mechanics.

Another thing I would like to say is, just because you know the fundamental physical laws of mechanics, electrical forces, and quantum mechanics, does that suddenly make the fields of chemistry and everything else in life suddenly unimportant to semantic classification and specialization? Does it also make teaching the course of mechanics superflous after one discusses the simple postulates of Newton (you know the right answer, I don't mean to sound condescending - just phrasing things like this is purely for pedagogy)?




Also, note that you are studying an old theory from the 19th century. "Thermodynamics" is sometimes referred to as "classical thermodynamics" to draw a line between the more modern interplay of quantum mechanics, classical mechanics, and statistics (in a subject called "statistical mechanics") to explain the same concepts of entropy, temperature, pressure, etc. This classical subject in its own domain is still correct, very useful, and pedagogically significant, so it's still taught in introductory physics courses even though it can be stated in a more fundamental way.

 

[Studiot]

I have just completed an intermediate course in classical mechanics. I am very comfortable with the subject, and I really enjoy solving the problems. I just love the idea, of describing everything in nature in terms of forces and their resulting accelerations.

Congratulations I'm glad you enjoyed it.

The classical mechanics you studied is about assemblages of point particles, but classical fluid mechanics is not. Classical fluid mechanics is a branch of continuum mechanics where the structure of the 'fluid' might be finely granular or it might be truly continuous. The analysis works out to be pretty well the same in either case. In other words fluid mechanics deals with a wider range of material/

Clasical thermodynamics is the same. It does not matter whether your system comprises an assemblage of particles, a continuum or a single particle the analysis is the same. Certain characteristic properties have been extractected that do not depend upon structure so if man ever has to apply the result to something non particulate it will still work.

The link or correlation between statistical mechanics and classical thermodynamics is no less satisfying for all that. But remember that a single particle in a bottle does not exert a classic pressure on its walls.

 

[AlephZero]

What are the thermodynamic phenomena that classical mechanics (simple collisions) cannot explain?(not considering any quantum effects) Can thermodynamics be thought of as a subset of classical mechanics?

Everythnig in classical mechanics is reversible. At the macroscopic level, most processes in the real world are NOT reversible.

One of the simplest "non-reversible" processes is the experimental fact that heat flows form hot stuff to cold stuff, but not the other way round. That's the starting point for the difference between classical mechanics and classical thermodynamics.

You can think of the whole of classical mechanics being derived from Newton's laws of motion. For thermodynamics, you add some more fundamental laws (not attributed to anyone person, but numbered like Newton's laws are numbered) dealing with things that classical mechanics doesn't "know" anything about.

Of course you can create another layer of theory that (partially) explains the thermodynamics of an ideal gas in terms of moving particles - except that ideal guses don't become liquids or solids when they coold down, and you won't get very far in dealing with simple "real world" situations (like boiling a pan of water on a stove) if you your theoretical toolkit can't handle things like that...

You aren't the first person (or the last) who feels that compared with classical mechanics, thermodynamics seems an incomprehensible mess at first sight, but stick with it - it will start to make sense eventually!

 

[symbolipoint]

Just a sideline curiosity - what are the true, practical, honest prerequisite mathematics courses to understand Thermodynamics at the level which springwave is studying? I do not mean the officially listed prerequisites; I mean the real ones which should be included but are usually never listed for the course description.