How to calculate the pressure in a sealed vessel with water.

[Mr Matt222]

Hi,


I cannot find any equation to help determine the resultant pressure from heating water in a sealed metal container, all I find is PV-nRt which is only gas - We are heating doing this in part to pretreat biomass. sealed tube: vol =170cc containing 80ml.s water: tube heated to 180C. I need to find appropriate relief valve.

How do I determine pressure?

Please show calculations

I assume it does not matter how much water is in the tube, the "gas" part of the tube has no influence on the specific pressure generated by heat/water (?)



Thanks so much!

M

 

[russ_watters]

Welcome to PF!

There is no calculation to do here: just look it up on a steam table.

 

[Mr Matt222]

I was thinking the pressure has to do with temp and the vol of the cylinder -

If I heat up to 150C, a 200cc sealed container containing 100 MLs water, the pressure would be different if I heat up to 150C, 100 mls. of water in a 500 cc container... is this not correct? - if I continue to increase the size of the container, will not the pressure decrease?

but actually in my case, not all the water has converted to steam -

 

[russ_watters]

No, it is not correct. Steam has a certain vapor pressure at a given temperature, so a volume of water will boil until that pressure is reached.

As long as that pressure is greater than that provided by the air and not all the water boils, it will reach an equilibrium between water and saturated steam.

What you describe is not fundamentaly different from the operation of a steam heating system.

 

[PJC01]

Hi M,

Calculating the pressure in a sealed vessel with water involves using the ideal gas law, which is the equation you mentioned (PV=nRT). However, this equation can also be applied to liquids, as long as we take into account the density of the liquid.

First, we need to gather some information about the system. In this case, we know the volume of the sealed tube (170cc) and the temperature it will be heated to (180C). We also need to know the number of moles of water present, which can be calculated using the mass of water (80ml) and its molar mass (18.02 g/mol).

Next, we need to convert the temperature from Celsius to Kelvin (180C + 273 = 453K) and the volume from cc to m^3 (170cc = 0.00017 m^3).

Now, we can plug these values into the ideal gas law equation:

PV = nRT

P(0.00017 m^3) = (80 g / 18.02 g/mol)(8.314 J/mol*K)(453 K)

P = (80 g / 18.02 g/mol)(8.314 J/mol*K)(453 K) / 0.00017 m^3

P = 7,360,620 Pa

Therefore, the pressure in the sealed vessel with water at 180C is approximately 7,360,620 Pa.

It is important to note that the amount of water does affect the pressure, as the volume of the liquid will change with temperature. Additionally, the pressure will continue to increase as the temperature increases, so it is important to have an appropriate relief valve in place to prevent the vessel from bursting.

I hope this helps and please feel free to ask any further questions.

Best,