studiot

I'm trying to keep things simple to illustrate a fundamental point.
So please let's avoid dissipative forces of any description.

The first law requires work to be carried out across the system boundary.

yet you write

This is the 'common misconception' I am trying to highlight.

benit13

I am not claiming that the work done is not performed across a boundary. If you draw a control volume around the block and then work is performed on the block from somewhere outside (i.e. across the boundary), then you have to decide what kind of energy that work gets transferred to. If the work done goes into internal energy, then yes, the 1st law of thermal dynamics tells you how that work affects the internal energy and, using an equation of state of the material, you can calculate the increase in temperature of the block. However, if the work done does not go into internal energy, then the work done affects the system in a different way. In the case of the block in the bowl, the work done goes into the kinetic energy of the block, together with its control volume, and it accelerates/decelerates relative to its external environment according to Newton's laws. The internal energy is unaffected.

studiot

This is the misconception I was talking about.

The internal energy ( of the system enclosing the block) remains constant because no work is done, not the other way round.

Yes the potential energy of the block becomes kinetic energy of the block and yes, without friction, it will oscillate up and down the bowl for ever.

benit13

Eh? It sounds like language semantics to me. Who cares whether

1. Work is done on an object, some of that work is converted to internal energy, therefore its internal energy increases; or
2. An increase in internal energy is detected. There is no heat flow into the object, so some work must have been done on it that was converted to internal energy?

It's just a relationship between the equation of state of a material and its external influences.

Besides, I can push a block 1m horizontally with a force of 1N and perform 1J of work. Are you saying this is not work if it doesn't increase its internal energy (presumably because, for example, all the energy went into kinetic energy/sound/heating of surroundings)?

studiot

You mentioned the "work-energy theorem" or the "work energy principle" as some call it.

When this is invoked there has to be a force external to the system.
This would be the case if a smaller block were to be attached via a string dangling over the edge of the bowl so that it was lifted as the original block slid down the inside.

Work would then be transferred outside the system enclosing the original block, via the tension in the string.

Here is an extract from a readable description in Sears and Zemansky

University Physics Part 1 Mechanics and Thermodynamics.

Note carefully it excludes the case of the only force acting being gravity.

You are right that the issue doesn't usually arise in mechanical systems, however it is of extreme importance in the release of chemical potential energy.

A longish discussion of the subject, with some really cool pics of a girl on a snowsled, can be found in

Basic Chemical Thermodynamics

E B Smith

Oxford University Press

pages 1 - 9

Attached Thumbnails

 

Pmb

I love reading your posts, dude. Its as if I'm almost guaranteed to be pleased by what I read.

The subject has nothing to do with thermodynamics. What's troubling about the post is that the term smooth as its used in physics usually means that there is no friction or the friction can be neglected. The system is simple - The gravitational field can be taken to be uniform and one can ignore the source since the force is given. I.e. there are more than one configurations which can generate a uniform gravitational field or one can be approximated.

The gravitational potential is simply mgz. However since no details about the shape of the bowl is given we cannot state the exact details of the motion. If the bowl is parabolic in shape then the motion is exactly sinusoidal but if its circular then it can only be approximated for small displacements as sinusoidal.

I.e. work is constantly being done on the object changing between positive and negative.

Pmb

Since the force is conservative the energy will be conserved. What the system is seems to depend on what studiot claims it is.

studiot

Actually I didn't define the system, though I agree with benit's choice.

benit13

I have no problem with that definition of W', particularly if it is going to be used directly in the first law of thermodynamics. After all, gravitational potential energy tends not to affect the internal state of objects. Then I concede that for the case of the block in the bowl, no work is being done.

However, I don't understand why the definition of work in the text book doesn't include the work done by gravitational forces. After all, there is tidal heating of celestial objects, where gravity is the main reason for the increase in internal energy of an object (it's also called "internal friction"). Surely the work-energy principle would want to include this effect?

What other forces are omitted from the theorem? Does it omit other field-like forces like electric/magnetic forces of stationary/moving charged objects?

studiot

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