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Old Mar 13th 2018, 10:40 AM   #21
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Originally Posted by studiot View Post
Here is one way to look at it.

Consider a body in a gravitational field.
Imagine you had a means to clap your hands and isntantaneously drain or remove all of its internal energy.

It would still be in the same place after such removal.

So unless your removal also removed all of its mass, would it would still possess the same gravitational potential, would it not?

Tricky stuff

It could contain all sorts of potential energy as well as GPE... it might have elastic PE, or be a stationary/moving charged particle in an electric or magnetic field. The definition probably removes all of these things (not just GPE) because changes in GPE, elastic PE, electric field PE, magnetic field PE, etc., rarely cause changes in temperature of objects on Earth, so there's no point keeping track of it... why bloat your equation of state with terms that have virtually no impact on the internal temperature of objects? You want to restrict your definition of work done to include things that make a difference, like friction or an encounter with another body with a different temperature.

In my opinion, there's just energy exchanges. As long as you're keeping track of the energy exchanges into and out of your control volume, there's no issue; the rest is stamp collecting. I usually use "work done" as "energy exchanges between two bodies", but if someone wants to precisely define "work done" as something more specific in a system of interest, then fine.

Consider the following... there's nothing wrong with defining a control volume of arbitrary size and then defining your own equation of state that includes all relevant energy exchanges with objects outside of that volume. You can then use the laws of physics to keep track of the "temperature" of this system. For example, you could create a control volume the size of a solar system and then keep track of its "temperature". The "work done" on the system would have to be through external gravitating bodies (like meteors or whatever), which would change the motion of the internal bodies within the control volume and hence the internal energy. Your equation of state will have a W' that doesn't neglect GPE so you can actually keep track of the changes in internal energy caused by nearby gravitating bodies.

This would be consistent with statistical mechanics, which does the exact same thing but at smaller scales. If you define a control volume the size of a molecular ion, how do you define it's equation of state and therefore its internal energy? Well, you'd have to include "work done" to include everything that can impact it's internal motions, like encounters with nearby charged particles, collisions with other molecules, the fact that another particle might react with it and changes it's size and shape...
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Old Mar 13th 2018, 11:01 AM   #22
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Here's a tricky twist.

Suppose the block is made of ice at zero C and instead of a bowl we have a very long slope which levels off to a very long horizontal plane when the speed of the block reaches 700 m/sc

Does the ice melt?
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Old Mar 13th 2018, 11:03 AM   #23
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People generally have an inadequate understanding of Energy but benit13 is spot on. I created a webpage which describes the concept of energy here:
What is Energy?

Regarding potential energy: There are typically two kinds of potential energy. There's the potential energy of position and the potential energy contained within a system. For example: a charge particle in a conservative field of has potential energy associated with position. If the field is a uniform electric field in the z direction having strength E and the particle has charge q then the potential energy is U = qzE. If we now consider the source of the field and include that then our answer is different. If the total charge in a capacitor with capacitance C is Q then the internal energy is U = q^2/2C.

The rest is merely semantics, i.e. nothing of any value, interest or any great importance. The importance is understanding the nature of potential energy.
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Old Mar 13th 2018, 12:48 PM   #24
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Thank you for that perceptive view.

I would appreciate it if you would develop this theme further in relation to internal energy.

There's the potential energy of position and the potential energy contained within a system.
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