The discussion revolves around the application of the integral of vdP in calculating work in flow machines, contrasting it with the more familiar PdV expression used in cylinder-piston systems. Participants explore the context of flow systems and specific cases such as compressors.
Participants do not reach a consensus on the use of vdP versus PdV, with some agreeing on the applicability of the former in flow machines while others remain uncertain about the transition between these expressions.
The discussion includes references to specific thermodynamic principles and the context of flow systems, but lacks detailed mathematical derivations or assumptions that could clarify the transition between the two expressions for work.
This discussion may be useful for students and professionals interested in thermodynamics, particularly those studying flow machines and the application of work calculations in engineering contexts.
Chestermiller said:Is your system a flow system, such that fluid is flowing into the system and out of the system through inlets and outlets to a control volume? An example would be a nozzle.
Thank you very much, now I understand the concept, I'm working on how to do the balance in such a way that I can demonstrate it in this case.robphy said:
For a differential section of the compressor operating at steady state, the open system version of the first law of thermodynamics tells us the $$dW_s=dh=Tds-vdP$$ where h is the enthalpy per unit mass of gas, s is the entropy per unit mass, v is the volume per unit mass, and ##W_s## is the shaft work. For adiabatic reversible operation, ds = 0, so $$dW_s=vdP$$Emmanuel S said:Indeed. In fact, the problem was with a reversible compressor; the process was polytropic, and after performing the mass and energy balance, when calculating the compressor's specific work, the professor established w = ∫ vdP
And he said that for flow machines, the work took that expression, not PdV.