Relationship between intutions on energy

[leo.]

Hi all,

After reading Feynman's Lectures I see that his way to understand energy is as a conserved quantity. On the last days then I've seem Susskind's lectures on classical mechanics and he also defines energy like that. He says that energy is a conserved quantity, being able to characterize groups of states of a system.

So the subsets of the set of all possible states are each of them characterized by a certain amount of energy. That's all fine and it gives a nice understanding that the main point of energy is it's conservation.

I'm still struggling however to relate this intuition on energy with the most common ones. People usually see energy as capability of a system on doing things. Even the word energy as I google means "activity". And also, there are those intuitions like: "a particle in the gravitational field of Earth needs to receive external energy to be able to be lifted and overcome gravity".

How all of those intuitions on energy agree with the definition of energy simply as a conserved quantity? I know how to get the formulas, put then together and show that the total energy is conserved, that's not my doubt. My doubt is really on the intuition behind.

Thanks very much in advance.

 

[Drakkith]

I don't understand what you want to know. The formulas show you exactly how energy is conserved and how it applies to the usual definition.

 

[leo.]

My doubt is the following: defining energy as a conserved quantity, how can one recover all that intuition on energy as the capability of a system to do things? My point is that intuitively it doesn't seem to be a relation between those two ideas. I would like to know if there is someway to intuit this relationship.

 

[A.T.]

...the main point of energy is it's conservation.

It is the only point.

My doubt is really on the intuition behind.

And rightly so as intuition often fails. Better stick to the definitions.

 

[Drakkith]

My doubt is the following: defining energy as a conserved quantity, how can one recover all that intuition on energy as the capability of a system to do things? My point is that intuitively it doesn't seem to be a relation between those two ideas. I would like to know if there is someway to intuit this relationship.

Energy is not defined as a conserved quantity, it is defined as the ability to perform work. It is simply an observed fact that it happens to be conserved.

 

[phyzguy]

Try looking up the term "free energy". This is usually defined as "the energy of a system that can be used to perform useful work". This is usually what we mean in everyday discussions of energy. People talk about the "energy crisis", and the obvious question is "how can there be an energy crisis if energy is conserved?" The answer is that when we talk about a shortage of energy, we usually mean a shortage of "free energy". The free energy of a system is distinct from the energy of a system which is not available to do useful work. The distinction between total energy and free energy led Clausius and others to the concept of entropy. I suggest reading up on these terms, and I think it will answer your questions.

 

[ag048744]

Energy is a conserved quantity. It is neither created nor destroyed. The only way to change it is to change by form. Thus, the total energy of any closed system that obeys physical laws is always constant. It does not get more intuitive than that.

 

[Jano L.]

My doubt is the following: defining energy as a conserved quantity, how can one recover all that intuition on energy as the capability of a system to do things? My point is that intuitively it doesn't seem to be a relation between those two ideas. I would like to know if there is someway to intuit this relationship.

Work-energy theorem:

Work done by external forces on the system equals increase in its energy

$$
\sum_k \mathbf F_{ext} \cdot \mathbf v_k = \frac{d}{dt} \sum_k \frac{1}{2}m_k v_k^2 + U(\mathbf r_1, ..., \mathbf r_N);
$$
if the left-hand side is negative, the system is doing work on the external bodies and its energy decreases accordingly.

 

[Andrew Mason]

The fact that energy is conserved makes it "something". If it was not a conserved quantity, we could not talk about it transferring from one body to another or from one form to another.

As has been said, energy is defined as the ability to do work (which is to apply a force through a distance). It is a quantity that is associated with a body or system of matter that tells us the ability of that body or system to perform work. Some of that work may not be useful. Energy may, for example, be used to warm up a cold reservoir in a heat engine (doing work on molecules) so that heat flow can produce useful mechanical work. But because energy is conserved in some form, its parts can all be accounted for so it can be thought of as "something".

Entropy, on the other hand, is not conserved. Entropy is not easy to conceptualize as a "something", despite the attempts by some to make us believe that entropy "flows". It will drive you nuts if you try to conceptualize entropy as "something". Entropy is best understood as an attribute of a thermodynamic system. Because it is not conserved, entropy is not something that comes from somewhere and goes somewhere or does something.

AM

 

[leo.]

So, let's see if I understood it well: since mechanical energy is defined to be kinectic energy plus potential energy we end up saying that the potential energy is a measure of the ability to perform work because if there is potential energy it can change, and when it changes by conservation of energy the kinectic energy can also change and so by the work-energy theorem work will be performed. Is this right?

This however, is something I fail to grasp when there are more forms of energy involved. If we sum all of them up and one of them changes, this doesn't imply directly that the kinectic will change performing work. It could very well be a change in any of the other forms compensating right?

Now there is something that gets me curious. Historically how people found out all of those concepts, like work, kinectic energy, potential energy, and so on, and how they found out they were all related? I know that there was an early discussion by Liebnitz on "vis viva" or "living force" of a system defined to be twice the kinectic energy, but I know nothing more than this.

 

[Andrew Mason]

So, let's see if I understood it well: since mechanical energy is defined to be kinectic energy plus potential energy we end up saying that the potential energy is a measure of the ability to perform work because if there is potential energy it can change, and when it changes by conservation of energy the kinectic energy can also change and so by the work-energy theorem work will be performed. Is this right?

All fundamental forces are conservative and all forces consist of some combination of fundamental forces. This means that total energy, in all forms, is conserved: ie. it is constant. If kinetic energy disappears it must be accounted for by an increase in potential energy, and vice versa. Some of that energy, however, may be used to do work on molecules and it takes the form of random molecular kinetic (thermal) energy, which is very hard to get back in a form to that is useful.

This however, is something I fail to grasp when there are more forms of energy involved. If we sum all of them up and one of them changes, this doesn't imply directly that the kinectic will change performing work. It could very well be a change in any of the other forms compensating right?

Kinetic energy of a body can be used to apply a force through a distance to another body. For example, a car coasting up a hill uses its kinetic energy to do work against the force of gravity that exists between the car and the earth. As it goes up the hill it gains potential energy in the same amount that that it loses in kinetic energy (ignoring the work done on the molecules in the air and the road - i.e. heat).

Now there is something that gets me curious. Historically how people found out all of those concepts, like work, kinectic energy, potential energy, and so on, and how they found out they were all related? I know that there was an early discussion by Liebnitz on "vis viva" or "living force" of a system defined to be twice the kinectic energy, but I know nothing more than this.

The importance of energy was not fully understood and appreciated until the 19th century with the experiments of James Joule. So don't feel bad if you have to do a lot of (mental) work to really understand energy.

AM

 

[AlephZero]

Try looking up the term "free energy".

Be careful - if you look up "free energy" on Google, you are more likely to get a list of crackpot sites than somewhere that will teach you physics.

 

[sophiecentaur]

I think Feynman did us a bit of disfavour, aamof, when he used words that have special meanings in the field of Physics as if their meanings were the same as in everyday life. He did the same thing with the word Photon, too. People have picked up on his statements as if they actually understood them and, often, they have spread around their misconceptions, thinking they had Feynman's approval.
I just don't think he understood just how limited we, mere humans, are about these matters. It was all crystal clear to him.