The relationship between temperature and pressure for water?

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Discussion Overview

The discussion revolves around the relationship between temperature and pressure for water, particularly in the context of a solar collector project. Participants explore thermodynamic processes and seek to establish accurate values for pressure and temperature in a controlled volume system involving water and molten salt.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant seeks an equation relating temperature and pressure for water at constant volume, aiming to confirm the accuracy of their values for a solar collector project.
  • Questions arise regarding the fluids involved in the system, particularly the pressure values of 100 bar before the turbine and 1.5 bar after, which some participants find unrealistic.
  • Another participant notes that at 510°C, water behaves similarly to an ideal gas, and discusses the implications of phase changes between liquid and gas water, suggesting the use of a phase diagram for better understanding.
  • There is a repeated emphasis on the need for realistic values for pressure and temperature based on the phase diagram, with acknowledgment that liquid water is essentially incompressible.
  • Participants express confusion about determining values for different segments of the system, particularly regarding mass flow rate, temperature, pressure, work of the pump, turbine, and heat transfer in the heat exchanger.
  • One participant mentions that mass flow rate remains constant if there is no accumulation, but notes insufficient information to determine pressure and temperature accurately.
  • References to the Carnot engine are made, suggesting it as a theoretical framework for understanding efficiency limits in the system.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the accuracy of the proposed pressure values or the methods to determine the necessary thermodynamic parameters. Multiple competing views and uncertainties remain regarding the relationship between temperature and pressure in the context of the project.

Contextual Notes

Participants highlight limitations in the available information, particularly regarding the assumptions needed to accurately determine pressure and temperature values. The discussion also indicates a dependence on phase diagrams and the complexities of the system setup.

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I have been looking everywhere for some equation that relates temperature and pressure at a constant volume for water. I am doing a project where I am designing a solar collector and it's thermodynamic processes and I want to ensure my values are accurate in a controlled volume. Attached is the diagram of my project thus far. Any help with regards to a confirmation of the accuracy of these values or an equation to find more accurate ones would be appreciated. Thanks!

NOTE: These values are ones I made up, my goal is to find better more reasonable values.

mb03z7.jpg
 

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what are the fluids involved?
Is the pressure really 100 bar before the turbine and 1.5 bar after?
 
Khashishi said:
what are the fluids involved?
Is the pressure really 100 bar before the turbine and 1.5 bar after?
The top loop is water and bottom loop is your average molten salt. These values are ones I made up in a system. The 100 bar to 1 bar seems unrealistic and that's why I am trying how to find more realistic values for this project.
 
510C is above the critical temperature for water, so water will be similar to an ideal gas at that point. Liquid water is essentially incompressible. If the temperature drops to the boiling point, some steam will condense into water, bringing the pressure down, dropping the boiling point. So the boiling point will follow the temperature for a while, and you will have some combination of liquid and gas water. So look at a phase diagram for water, and take a look at w

I modified http://commons.wikimedia.org/w/index.php?title=User:Matthieumarechal&action=edit&redlink=1 's CC diagram off of wikipedia. The yellow-orange roughly shaded region is the range of densities and temperatures you might expect. The details will depend on all sorts of details of the setup. If you have a combination of liquid and gaseous water after the cooler, then you will lie somewhere on the liquid/vapor phase boundary line.
 

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Khashishi said:
510C is above the critical temperature for water, so water will be similar to an ideal gas at that point. Liquid water is essentially incompressible. If the temperature drops to the boiling point, some steam will condense into water, bringing the pressure down, dropping the boiling point. So the boiling point will follow the temperature for a while, and you will have some combination of liquid and gas water. So look at a phase diagram for water, and take a look at w

I modified http://commons.wikimedia.org/w/index.php?title=User:Matthieumarechal&action=edit&redlink=1 's CC diagram off of wikipedia. The yellow-orange roughly shaded region is the range of densities and temperatures you might expect. The details will depend on all sorts of details of the setup. If you have a combination of liquid and gaseous water after the cooler, then you will lie somewhere on the liquid/vapor phase boundary line.

Hmm, I'm still a bit confused. I still am having trouble finding values for each segment of the system. Going off the assumption that “…steam inlet conditions of 510°C, 10 MPa, and a flow rate of 50,000 kg/hr” how can I effectively find the mass flow rate, temperature, and pressure of each segment? Also what is the best way to find the work of the pump [new in diagram 2] and the turbine as well as the heat transfer of the heat exchanger. I have attached a new hopefully more clear diagram.

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Mass flow rate is equal everywhere if it's not bunching up. There's not enough information for pressure and temperature, but you can get a rough range of values based on the phase diagram.
 
Khashishi said:
Mass flow rate is equal everywhere if it's not bunching up. There's not enough information for pressure and temperature, but you can get a rough range of values based on the phase diagram.
Hmm, with only the values given in this diagram, what would you choose for the remaining segments in order to find W and Q?
 

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Read up on a Carnot engine. Your real engine won't be as efficient, but it does put some limits on what is possible.
 
Khashishi said:
Read up on a Carnot engine. Your real engine won't be as efficient, but it does put some limits on what is possible.
I'll do some reading and get back to you.
 

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