Work Transfer

preamble:

In mechanics , work is defined as the scalar product of the force vector and the displacement vector of its point of application. As we develop the subject of thermodynamics we will find that this definition of work is inadequate , that is , it fails to cover many other types work interaction which are fully convertible to one another and to mechanical work. Thus a thermodynamic system can do work without exerting a ' mechanical ' force which moves a point of application.

The thermodynamic definition of work:

An interaction between a system and the surroundings is a work interaction if , during a given process , if the only effect outside the system could be reduced to one of the raising(or the lowering) of a weight. 

To show that a system does work during a given process , we replace the normal environment of the system by a device which can interact with the system during an identical internal process , and raise(or lower) a weight as the one and only result of the interaction. 

Work during boundary expansion:

If a system which is in internal equilibrium expands slowly , the rate of expansion being such that the increase in kinetic energy of the system or any part of the surroundings is negligible , the work transfer from the system to surroundings for an element increase(δV) of the volume is given by ;

-δW = p δV

where the p is the pressure of the system at the instant when the volume is V. Work is written with a negative sign because the notation that work done on the system is positive. The above expression also be written as ;

-dW = p dV

The total work during any finite process 1-2 can be found by integration of the above expression. 

Other types of work:

Besides systems which under go a volumetric expansion , there are others which may be of engineering interest. In all these ;

dW = force(F) . displacement(dX) 

Here the concept of force has been generalized to include the appropriate intensive properties , and the displacements(X) are conjugate extensive properties the change of which constitute displacements associated with the 'force' F.