The relationship between temperature and pressure for water?

In summary, I am having trouble finding an 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. 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!
  • #1
Tapehead2
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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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  • #2
what are the fluids involved?
Is the pressure really 100 bar before the turbine and 1.5 bar after?
 
  • #3
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.
 
  • #4
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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  • #5
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.

11vr8sz.png
 
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  • #6
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.
 
  • #7
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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  • #8
Read up on a Carnot engine. Your real engine won't be as efficient, but it does put some limits on what is possible.
 
  • #9
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.
 

Related to The relationship between temperature and pressure for water?

1. What is the boiling point of water at different pressures?

The boiling point of water changes with pressure. At sea level, where the pressure is 1 atmosphere, water boils at 100 degrees Celsius. As pressure increases, the boiling point also increases. For example, at the top of Mount Everest where the pressure is lower, water boils at around 68 degrees Celsius.

2. How does pressure affect the freezing point of water?

As pressure increases, the freezing point of water decreases. This is because pressure compresses the molecules of water, making it more difficult for them to form into a solid. This is why water can remain liquid at temperatures below 0 degrees Celsius in deep oceans where the pressure is much higher.

3. Why does water boil at a lower temperature at higher altitudes?

At higher altitudes, the air pressure is lower, which means there is less atmospheric pressure pushing down on the water. This results in a lower boiling point, as less pressure is needed for the water molecules to escape into the gas phase.

4. How does the temperature of water affect its vapor pressure?

The vapor pressure of water increases as its temperature increases. This is because at higher temperatures, the water molecules have more energy and can escape into the gas phase more easily, creating a higher vapor pressure.

5. What is the relationship between temperature and pressure for water?

The relationship between temperature and pressure for water is an inverse relationship. This means that as temperature increases, pressure decreases, and vice versa. This relationship is known as the ideal gas law, which states that pressure is proportional to temperature when volume and amount of substance are held constant.

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