# Definition of a system in flow processes

In classical thermodynamics the state of a system (pressure, temperature etc.) can only be specified if it is in equilibrium. My understanding of equilibrium leads me to believe that the state is uniform over the whole system i.e if we looked at a smaller subsystem of the larger system the state would be the same. Therefore, we are able to analyse a thermodynamic process if we assume that it is in equilibrium at every step. This is conceptually easy to grasp in the case of a closed system such as a piston and cylinder, where properties of the working fluid such as temperature are uniform over the whole system at any stage of the process.

This begs the question: in a process where the working fluid is mobile, where exactly do we draw the system boundary? In a turbine, for example, the state of the working fluid at the outlet differs from the inlet and everywhere in between. Therefore, the state of the system (assuming the system is defined to be the turbine itself) cannot be determined because it is not in equilibrium. So what is the system?

For analysing a closed system, the system should be in the equilibrium state and at a particular point of time, we can express the state of the system using thermodynamic coordinates (such as p,v).

But in case you are analysing an open system(executing flow process such as turbine or compressor), this is not the case. In an open system we are more concerned about the rate of change of properties and if you consider the entire turbine as the open system/control volume, you can use the Reynolds transport theorem to evaluate the rate of change of extensive properties which is given by

$\frac{dN}{dt}=\frac{\partial}{\partial t}\int_{cv}\rho \eta d\forall+\int _{cs}\rho \eta \overrightarrow{v}\cdot d\overrightarrow{A}$

where N is an extensive property and $\eta$ is the corresponding specific extensive property.

For an open system like a turbine, we use the open-system version of the 1st law of thermodynamics. Clearly, as you point out, such a system could not be considered as being in thermodynamic equilibrium. But, in applying the open-system version of the 1st law to such a system, we invoke an additional approximation: the fluid within the system is locally close to being at thermodynamic equilibrium, such that the usual thermodynamic functions of internal energy, enthalpy, entropy, etc. can be defined locally (i.e., per unit mass). This approximation has been broadly found to be quite accurate, and enables us then to accurately quantify the behavior of fluids passing through open systems.