Rankine Cycle $pV$ diagram

I was going through the $$pV$$ diagram of the ideal Rankine cycle and all of the images that I found on the internet and as opposed to the $$TS$$ Diagram, they tend to show the compression in the feedwater pump (that's between condenser and boiler to raise the water pressure to boiler pressure) to be an isochoric process while instead in an ideal Rankine cycle, it's an isentropic compression within the pump. For example, look at this diagram.

Process 1-2 which is the isentropic expansion in the turbine is depicted correctly but process 3-4 that's isentropic compression in the pump is in fact shown as isochoric.

Process 3-4: The water from the hot well or the surge tank which is at low pressure is pumped into the boiler at high-pressure p1. Here pumping process 3-4 is isentropic.

While it's not as per the diagram. Can anyone provide some clues?

• Minor comment to the post (v2): Please consider to mention explicitly author, title, etc. of link, so it is possible to reconstruct link in case of link rot. May 28, 2022 at 8:16

but process 3-4 that's isentropic compression in the pump is in fact shown as isochoric.

There's no contradiction here. A process can be both isochoric and isentropic.

In this case it's considered isochoric because liquid water is considered to be incompressible for the range of pressures involved. So the pump is not considered to decrease the volume of the water. It is providing the necessary pressure to force the water from the lower pressure condenser into the higher boiler pressure.

It is considered isentropic because the process is carried out both reversibly and adiabatically.

Hope this helps.

• That first equation only applies to an ideal gas isentropic process. May 28, 2022 at 12:46
• And your last equation only applies to an ideal gas isothermal (constant temperature) process. May 28, 2022 at 12:50
• Ok, I understood. By second law of thermodynamics, a process could be both isentropic and isochoric and as well as isothermal for an incompressible fluid only. May 28, 2022 at 12:52
• What kind of isothermal process for an incompressible fluid that is also isentropic did you have in mind? May 28, 2022 at 13:50
• What I'm saying is if a reversible process is both isothermal and adiabatic, then it is also isentropic. However, off hand I'm not aware of such a process. If you can identify one, I would appreciate it if you would let me know. May 28, 2022 at 15:58