# Work in mechanics vs. work in thermodynamics

1. Feb 2, 2006

### Leon4735

Hi,

I am wondering how I can reconcile the concept of work as it is
introduced in mechanics with the way work is defined in thermodynamics,
as a transfer of energy. I would also like to maintain the convention
that negative work means a loss of energy, and positive work means a
gain of energy. The example I have been considering is an object
falling toward the surface of the Earth. In most textbooks, it seems
that the object+Earth as an isolated system in which mechanical energy
is conserved. Does the concept of work have any meaning in an isolated
system? When an object falls the gravitational force acts along a
displacement, so it seems like work is done by the gravitational force
on the object. If so, where is the energy being transferred from? If it
is transferred from the gravitational field, the field loses energy;
shouldn't the work done by gravity be negative? But the force and
displacement of the object are in the same direction, so a conventional
calculation gives a positive work.

If anyone has any thoughts as to how these ideas can be made
consistent, or where my thinking is flawed, I would greatly appreciate
it.

Thanks - Leon

2. Feb 2, 2006

### Staff: Mentor

What makes you think the definitions are different?

If positive work is done on a system, then the system gains energy (all else being equal).

Why not? Work is a means of transferring mechanical energy from one part of the system to another. (Of course, no net work is done on the object+Earth system as a whole.)

Yes, gravity does positive work on the falling object, thus increasing its kinetic energy.
Yes, the field loses energy; it does so by doing positive work on the object.

3. Feb 3, 2006

### vaishakh

Energy is requeired to perform work. So a one or the other sort of an energy is lost by a system which does some work. However internal reactions in the system are not considered as work. For example if you have an Earth + body as a system, and then the body falls on earth, the systemhas no efect on external object, as well as vice versa, external objects have no interaction on this. Thus no wrk is being done by the Earth + body sytem. Similarly if some work is done on a sytem, the energy required to perform that work on the system is gained by the system. For example, in the previous case if body was your system, earth collides on the body owing to the gravitational force applied by the Earth. Now this is an external force. And thus the body has gained energy, in the form of Kinetic energy. It has lost no energy because potentialenergy is defined only in the Earth + body system. As earth collides on the body, if the collision had been partly ellastic, some mommentum is transferred back oon earth, and some Kinetic energy is lost to earth in the form of heat, or that is the work done by the ball on earth due to the free fall.
Thermodynamics deals with solving the difference in energy levels of a system by measuring the energy required to perform cerian things. But mechanics deals with solving the dynamics of a system by calculating the difference. Hope I have made your doubt clear.

4. Mar 22, 2010

### mikyway

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