Differential Equations for a Gas-Filled Chamber System

[Xtof]

I'm trying to figure out which set of differential equations describe the following quite general but relatively simple system:

A chamber which volume can be changed by moving a piston filled with a gas. Additionally, gas can be released from the chamber through a relief valve and heat can be added/extracted through the chamber walls.

State of the system described by a certain molar mass of a gas n occupying a volume V at pressure P (assume ideal gas).

The question thus is: what are the differential changes in pressure dP for given differential changes in volume dV, molar mass dn and heat dQ.

In other words: how does this system evolve when volume and mass are simultaneously varied while heat is supplied/extracted?

Additionally, which equations describe the evolution of this system for a non-ideal gas which heat capacities are general functions of temperature (Cp(T), Cv(T)).

I have a basic knowledge of thermodynamics and assume you need to use concepts of internal energy and enthalpy but I cannot figure out how to apply them since neither volume nor pressure are constant.

Thanks for your assistance or discussion!

Christophe

 

[xHossx]

You could try googling '1st law of thermodynamics open system'. (I found this: http://www.tech.plym.ac.uk/sme/ther103/ther103-first law open systems.pdf.)

The equation in the center of page 5 pretty much summarizes it all. Should be pretty easy to understand if you're familiar with closed systems already.

I'd tell you more, but it's been a long while since I had to think of similar problems. Also, the inlet velocity would be zero. And you should be able to substitute the work and mass rates and changes in enthalpy with expressions that have dP, dV, dT, and dn in them.

I'm not too sure about the pressure relief valve (and maybe a few other things as well). Could be I'm seriously oversimplifying, in fact, but this should get you going somewhat, at least.