# Work exchanged by a system, and internal forces' work

• MathError
In summary: But I'm not sure.Thanks for your help.In summary, the book explains that when a system receives a force from the environment it will react with a force from the system to the environment. Internal forces do not do work in these cases, but if the system is not a solid body, they will. The equation W(e-s)=-W(s-e) is true if there are no forces of friction, but in general you have to consider the work of these forces. The book does not explain how it comes to this equation. An example is given, but I doubt it is correct. Internal forces do work in case 3, but the work of F(e-s) does not coincide with the work of
MathError

## Homework Statement

Hi to everyone, I'm studying thermodynamics, especially I'm focused on the work exchanged by a system. Book's explanation says that when the system received a force from the environment [F(e-s)] (on its surface) it reacts with a force from the system to the environment [F(s-e)]. Because of Third Newton's law F(e-s)=-F(s-e).
These forces act for the same displacement so
W(e-s)=-W(s-e).

I think I understood these points but I'm not so clear about the following part of explanation.

The equation W(e-s)=-W(s-e) is true if there are no forces of friction.
In general you have to consider the work of these forces.
In presence of forces of friction the equation W(e-s)=-W(s-e) becomes:
W(e-s)=-W(s-e)-W(T(s-e)) [W(T(s-e)) represents the work of force of friction from the system to the environment].
The book doesn't explain how it comes to this equation so I tried to write an example, but I dubt it's correct.

In all these cases the system is rigid so the internal forces of the system doesn't do work. However if the system is not a solid body, internal forces do work.

This is the point where I find more difficulties.
From dinamics I know the resultant of the internal forces [R] is zero but they can do work beacuse internal points can cover different displacements.

Now I'm a bit confused.

The book distinguish the internal forces from forces from the system to the environment
[F(e-s)]. My question is: are F(e-s) produced by internal forces?
I don't think so, because R=0, but at the same time I imagine that internal stress of the system causes these forces on the surface.
If F(e-s) are produced by internal forces, does the work of F(e-s) coincide with the work of internal forces?
Sorry for the bad english but I tried to as clear as possible.
I hope you can help me.
Thanks

## Homework Equations

F(e-s)=forces from the environment to the system
F(s-e)=forces from the system to the environment
T(s-e)=forces of friction, from the system to the environment
T(e-s)=forces of friction, from the environment to the system
W(e-s)=-W(s-e)
W(e-s)=-W(s-e)-W(T(s-e))

## The Attempt at a Solution

These are the examples I did to try to understand the different cases
https://ibb.co/n3sy9Pr

https://ibb.co/njK8R2TIn case1 the forces of friction don't do work, so we have W(e-s)=-W(s-e).In case2 the point 1 is at rest and the point 2 is displaced with the same velocity of point A, so the internal forces don't do work (because points are displaced with the same velocity), so we have again W(e-s)=-W(s-e).In case3 the internal forces do work because point 1 and point 2 covers different displacements. This is the part where I'm more confused.If F(e-s) are produced by internal forces, does the work of F(e-s) coincide with the work of internal forces?I think that in this case we have:W(e-s)=-W(s-e)-W(internal forces).

## 1. What is work exchanged by a system?

Work exchanged by a system refers to the transfer of energy between the system and its surroundings. This can occur in various forms, such as mechanical, electrical, or thermal work.

## 2. What are internal forces' work?

Internal forces' work refers to the work done by forces within the system itself. These forces can include tension, compression, and shear forces.

## 3. How is work exchanged by a system calculated?

The work exchanged by a system can be calculated by multiplying the force applied by the displacement of the system in the direction of the force. This is represented by the equation W = F * d.

## 4. What is the relationship between work and energy in a system?

Work and energy are closely related in a system, as work is a measure of the transfer of energy. When work is done on a system, its energy increases, and when work is done by a system, its energy decreases.

## 5. Can internal forces do work on a system?

Yes, internal forces can do work on a system. This occurs when the system experiences a displacement due to the internal forces acting on it, resulting in a transfer of energy within the system.

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