How to justify the thermodynamic work in a turbine is VdP?

What is thermodynamic work?

Thermodynamic work can be categorized into two types - work at constant pressure (PdV) and work at constant volume (VdP).

In the case of work at constant pressure, the system undergoes a change in volume while the pressure remains constant. This type of work is often associated with processes occurring in closed systems, such as a piston-cylinder arrangement. On the other hand, work at constant volume involves a change in pressure while the volume remains constant. This type of work is commonly associated with processes occurring in open systems. Turbines are considered an open system.

Both types of work are related to the change in enthalpy (dH) of the system. For work at constant pressure, the change in enthalpy is given by dH = q - PdV, while for work at constant volume, the change in enthalpy is given by dH = q + VdP.

How a turbine is idealized as an isentropic [ adiabatic + internally reversible] process

The adiabatic nature of the process ensures that there is no heat transfer, thus no external entropy generation. Additionally, the work done within the blades (expressed as VdP) doesn't contribute to internal entropy generation, as the steam already occupies the space within the blades. This internal VdP work within the blades is effectively a pressure-volume process and doesn’t involve any change in the entropy within the system. Therefore, both the external and internal characteristics of the turbine process contribute to minimal entropy generation, making it an isentropic or near-isentropic process.

Explanation by Mollier’s H-S diagram

On a H-S diagram, a vertical straight line represents a process with no change in entropy. This means that the specific entropy of the substance remains constant throughout the process. in the context of a steam turbine, if the process is represented by a vertical line on the H-S diagram, it implies that there is no change in entropy as the steam passes through the turbine stage. Now, to relate this to the VdP work and the absence of volume change inside the turbine:

- The VdP work, where "V" denotes volume and "P" denotes pressure, generally signifies work done against a constant volume.

- In the case of a steam turbine, when a vertical line appears on the H-S diagram, it indicates that the process within the turbine is occurring at constant entropy, which implies that the volume is not changing during the expansion process. So, the absence of entropy change indicated by a vertical line on the H-S diagram aligns with the concept of constant volume (V) work, as it reflects the conditions conducive to VdP work, where the volume of the substance remains constant during the process. Therefore, by analyzing the H-S diagram in relation to the VdP work and the lack of entropy change, engineers and thermodynamic specialists can gain insights into the specific thermodynamic processes occurring within the steam turbine and make informed decisions regarding its design, operation, and efficiency.

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