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In many diagrams of coal, gas or nuclear power plants, a steam turbine is shown as part of a closed loop system.

(Search "power plant diagram" - this one illustrates the point well.)

I recall seeing such diagrams as a high school student, and at the time I considered that something was not quite right about it - although I don't recall raising the question as I assumed I would learn it in more detail at a later date and my question would be answered.

I now have a degree in physics, and my question is still not answered - so here goes.

What bothers me about this diagram is the closed loop between the steam generator and the turbine. When steam is generated in the steam generator, the pressure will increase. Looking at the image I provided a link to, the author has depicted a tank half full of water and half full of steam. There is a pipe at the top "where steam goes out" and a pipe at the bottom "where water comes in". However the pressure at the bottom and the top is the same. (Actually not quite, due to gravity acting on the water, the pressure at the bottom is greater.)

If steam flows through the turbine, presumably the pressure is lower at the output.

The diagram then depicts a condenser, where the pressure presumably must also be less.

The steam condenses to water and is then pumped back into the bottom of the boiler.

This part bothers me. Energy is being used to pump the water back into the boiler. It must presumably be quite a lot of energy, since work is being done against a great pressure.

I would guess that the type of pump used is similar to that of an air compressor, ie one that runs in cycles, rather than like a "fan". If this is the case, then it would be ok to have a very large pressure difference either side of the pump without a lot of energy wasted.

If everything I have described above is correct, then it must be that energy is generated (in the turbine) only from the thermal and kinetic energy of the steam. It must be the case that we have to put pressure energy back into the system via the pump to maintain a flow of steam. (Or else we would run out of water.) The reason for this is without the pump, we have a boiler connected to two ends of a turbine in a loop. If we boil water in the boiler, increasing the pressure, then the pressure increases the same at both ends of the turbine, and there will be no flow. So obviously this wouldn't make sense, the turbine wouldn't rotate and no electrical energy would be generated.

It must be the case that the kinetic and thermal energy extracted is more than the pressure energy re-inserted. How can we prove (or demonstrate) this?

Is the diagram an accurate representation of a real system or is some critical information missing?

So my question is how do we analyze this system? With my very elementary knowledge of thermodynamics I don't know where to start. I didn't do much thermodynamics at University, and I don't think I was particularly good at the simple things I did understand such as Carnot engines.

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  • $\begingroup$ A diagram would be helpful. In addition, as Chet Miller noted in his answer, this is a chemical engineering design problem. Also note - this is not a totally closed system. There is boiler "blow down" to eliminate contaminants from the system, and treated boiler make-up water that is used to maintain the material balance. $\endgroup$ – David White Jul 4 at 0:25
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Detailed analysis of the kind of Rankine power cycle you are describing can be found in most decent thermodynamics textbooks, including Fundamentals of Engineering Thermodynamics by Moran et al and Introduction to Chemical Engineering Thermodynamics by Smith and van Ness. The actual amount of energy required to pump liquid water from the low pressure of the condenser to the higher pressure of the boiler is tiny. This is because the specific volume of liquid water is extremely small compared to that of steam. The rate of doing work by the pump can be estimated by multiplying the pressure change across the pump by the mass rate of flow of liquid. The main source of energy supplied to the turbine comes from the heat added to the boiler to vaporize the water and discharge it at a high pressure. The drop in pressure from one end of the turbine to the other enables the flowing steam to cause the turbine blades to rotate and deliver electrical energy by turning a generator.

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