# Water Pressure in a Sealed Vessel

• Dyslexic Poet
In summary, the discussion revolves around determining the pressure of a reaction that will take place in a steel pressure vessel with an inner Teflon container. The container will be filled with 240 mL of water at a temperature of 250°C, where the head-space pressure is approximately 40 bar. The conversation also mentions calculating the pressure using the compressibility and bulk modulus of water, but the values obtained seem unreasonable. The discussion also touches on the expansion of the container and the water at high temperatures.
Dyslexic Poet
Hello,

I am a PhD student in chemistry, and need to determine the pressure of a reaction to be carried out

I have a steel pressure vessel with an inner Teflon container (total volume = 270 mL) which is placed in an oven at 250°C. I wish to put 240 mL of water into this container (along with 1 g of material). At this temperature, I know that the head-space pressure to be approximately 40 bar. However, the relative specific volume of water at 250°C (to that at RT) is 1.25. I believe this means that my water wants to take up a volume of 300 mL. As this is 30 mL larger than the container itself, I am not sure if it will therefore be exerting an extra pressure much larger than the head-space pressure.

I've tried a few different ways to calculate a value for this second pressure, but to no avail. One was to use water's compressibility and bulk modulus, but keep ending up with a value upwards of 2500 bar, which is just ridiculous.

Any help would be appreciated in helping me solve my problem. Please ask if I have left out any information required of the system.

Thanks,

Dyslexic Poet said:
I've tried a few different ways to calculate a value for this second pressure, but to no avail. One was to use water's compressibility and bulk modulus, but keep ending up with a value upwards of 2500 bar, which is just ridiculous.

If the liquid wants to occupy a volume greater than the 270 cc that you have available for it, that number is not at all unreasonable. Liquids are pretty much incompressible.

To really appreciate just how incompressible liquids can be, you have to tear down and rebuild an automobile engine that has been destroyed by hydrolock: If the volume of the combustion chamber at maximum compression is 40 cc and somehow you've allowed more than 40 cc of liquid into the cylinder before the piston comes up... The piston doesn't come up and compress the liquid down to 40 cc. Instead, the piston stops cold and the connecting rod (which is a no-kidding serious piece of steel) bends or breaks.

The bulk modulus of steel is about 160 GPa compared with 2.2 GPa for water, but to get the "bulk stiffness" of the pressure vessel you have to reduce the 160 by a factor of the order of (thickness/length) of the vessel. So the effective bulk modulus of the vessel could be a similar order of magnitude as the bulk modulus of the liquid inside.

The fact that you would probably need to expand the volume of the pressure vessel by a few percent without bursting it should be enough to see this isn't a realistic situation, without doing a more "accurate" calculation.

Does the container also expand with temperature? By how much?

Chet

Thank you for the replies.

I can tell you that the width of the vessel walls are 10 mm. The Teflon container will expand, but I don't believe by any significant amount.

The same experiment has been carried out successfully (many dozens of times), in a similar container with a total volume of 90 mL (it's walls are 15 mm thick). For this, only 80 mL of water was used, so the ratios are kept constant. This vessel is sitting on my desk looking absolutely fine, which suggests to me that the pressure couldn't be that high.

I have this calculation, but I am dubious of it:

Volume of bomb: 270 mL
Volume of water at 20-25 C placed in bomb: 240 mL
Volume of water at 250 C: 1.25x240 = 300 mL (www.engineeringtoolbox.com/water-thermal-properties-d_162.html)

Isothermal compressibility of water, k: 4.8 x 10-10 Pa-1 (at 100°C - this value I believe to be incorrect, and I will explain in a moment why I am using its value at only 100°C)

k = - (1/V)(dV/dp)T
Δp = - (1/k) (ΔV/V) = (1/4.8x10-10)(30/270)
Δp = 2300 bar

The following link is to the site where I took this k value from (which unfortunately only goes up to 100°C): http://physchem.kfunigraz.ac.at/sm/Service/Water/H2Obetat.htm

However, I have in front of me three literature articles that state that at 100°C, k = 49.1 x 106 bar-1 (4.91 x 1012 Pa-1). Which is 20 orders of magnitude apart. My thermal physics knowledge runs out completely here, and have no idea which is right and why.

Last edited by a moderator:
Dyslexic Poet said:
Thank you for the replies.

I can tell you that the width of the vessel walls are 10 mm. The Teflon container will expand, but I don't believe by any significant amount.

The same experiment has been carried out successfully (many dozens of times), in a similar container with a total volume of 90 mL (it's walls are 15 mm thick). For this, only 80 mL of water was used, so the ratios are kept constant. This vessel is sitting on my desk looking absolutely fine, which suggests to me that the pressure couldn't be that high.

I have this calculation, but I am dubious of it:

Volume of bomb: 270 mL
Volume of water at 20-25 C placed in bomb: 240 mL
Volume of water at 250 C: 1.25x240 = 300 mL (www.engineeringtoolbox.com/water-thermal-properties-d_162.html)

Isothermal compressibility of water, k: 4.8 x 10-10 Pa-1 (at 100°C - this value I believe to be incorrect, and I will explain in a moment why I am using its value at only 100°C)

k = - (1/V)(dV/dp)T
Δp = - (1/k) (ΔV/V) = (1/4.8x10-10)(30/270)
Δp = 2300 bar

The following link is to the site where I took this k value from (which unfortunately only goes up to 100°C): http://physchem.kfunigraz.ac.at/sm/Service/Water/H2Obetat.htm

However, I have in front of me three literature articles that state that at 100°C, k = 49.1 x 106 bar-1 (4.91 x 1012 Pa-1). Which is 20 orders of magnitude apart. My thermal physics knowledge runs out completely here, and have no idea which is right and why.

The 4.8x10-10 is correct.

Incidentally, the coefficient of volume thermal expansion for teflon is 3x10-4 per degree C. So the volume of the teflon container will increase significantly also. See what happens if you take this into account.

Chet

Last edited by a moderator:

## What is water pressure in a sealed vessel?

Water pressure in a sealed vessel refers to the force exerted by the weight of the water within the vessel on its walls and base, as well as on any objects or substances present inside the vessel.

## How is water pressure in a sealed vessel measured?

Water pressure in a sealed vessel can be measured using a pressure gauge, which displays the force in units of pounds per square inch (PSI) or kilopascals (kPa). It can also be calculated by multiplying the density of water (1000 kg/m3) by the depth of the water in meters and the acceleration due to gravity (9.8 m/s2).

## What factors affect water pressure in a sealed vessel?

The main factors that affect water pressure in a sealed vessel are the depth of the water, the density of the water, and the acceleration due to gravity. Other factors can include the shape, size, and material of the vessel, as well as any external forces acting on the vessel such as temperature changes or external pressure.

## What happens to water pressure in a sealed vessel as depth increases?

As depth increases, water pressure in a sealed vessel also increases. This is because the weight of the water above exerts more force on the lower levels of the vessel, resulting in a greater pressure. For every 10 meters of depth, the water pressure increases by approximately 1 atmosphere (14.7 PSI or 101 kPa).

## How does water pressure in a sealed vessel affect objects inside?

The water pressure in a sealed vessel can have a significant impact on any objects or substances present inside. If the vessel is not strong enough to withstand the pressure, it may collapse or rupture. Additionally, the pressure can compress air pockets and cause objects to float or sink. It can also affect the boiling point of water, making it difficult to cook or sterilize objects inside the vessel.

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