Thermodynamic transformation

A thermodynamic transformation or process is a change to a physical system's thermodynamic state, going from one state of thermal equilibrium to another. They can be represented as paths taken in phase space. They may be reversible or irreversible: a transformation is said to be reversible if the system will retrace the exact path, only in reverse, if the external forces causing the transformation are themselves reversed. An irreversible one will instead not retrace the exact path, thus causing a permanent change in the system.

If the system transforms very slowly, it is possible to consider it as if it were in equilibrium throughout the transformation itself. This type of transformation is said to be quasi-static. Quasi-static transformation are usually reversible.

Types#

Specific transformations have been given special names:

For constant $T$ we have isothermal transformations. The path traced by one of these in phase space is called an isotherm.
For constant $P$ we have isobaric transformations.
For constant $V$ we have constant-volume transformations.
With no heat exchanged $\Delta Q=0$ we have adiabatic transformations.
Cyclical transformations start and end in the same state, for which $\Delta U=0$ .

Work done#

For reversible transformations, we can consider infinitesimal paths. The mechanical work done by the system over such a path is given by

dW=PdV

We can extend this to a path from points $A$ to $B$ in phase space by concatenating many infinitesimal paths together. The work done over this path therefore is

\Delta W=\int_{A}^{B}PdV

In a non-cyclical transformation, this is the area under the curve in the $PV$ graph. In a cyclical transformation, this is the area inside of the closed shape.

90%

This does not hold for irreversible transformations, whose work is usually not $\int PdV$ . For example, in the free expansion of an ideal gas, the system does not perform any work to expand, so $\Delta W=0$ despite the volume and pressure both not changing.

The purpose of normal, $A\to B$ transformations is to change the system's state. The purpose of cyclical, $A\to A$ transformations is that they produce heat from work, and since they are cyclical, they can be performed indefinitely provided there is work to be given. These form the core principle of a heat engine.