# 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?

$\frac{dN}{dt}=\frac{\partial}{\partial t}\int_{cv}\rho \eta d\forall+\int _{cs}\rho \eta \overrightarrow{v}\cdot d\overrightarrow{A}$
where N is an extensive property and $\eta$ is the corresponding specific extensive property.