How much steam is needed to open a relief valve using the ideal gas law?

[bionic6manuel]

I am trying to solve a problem but I am not sure if I am going about it the right way. I am using the ideal gas law to find out the amount of steam it will take to open a relief valve. Using the law I have calculated the amount of steam that will be in a volume but I am not sure if that is also the point the relief valve will open or is there a formula to account for the steam compression in the volume.

Data
volume of container = 213.75m3
area of container = 0.21375m2
steam temperature = 573 kelvin
thermal conductivity of five walls of container = 0.003 W/m/k
heat loss through one wall = 10 000 watts
relief valve = 86 bars

 

[jim hardy]

saturated steam is not ideal gas.

use steam tables to find specific volume of steam at your T & P.

 

[bionic6manuel]

thank you for your answer i thought that i should use steam tables. this is the way i thought of using the table. say the specific volume is 0.123m3 at a unamed Temp and Pressure and my container has a volume of 0.006m3. 0.123/0.006=? does the answer mean that the container will be filled up at ?. can i use the real gas law that takes into account the compresablity factor

 

[jim hardy]

specific volume is 1/density.

Sorry , i usually work in English units, cubic feet and BTU's and Fahrenheit
but i'll try.

at the temperature you gave in first post
573K


from this steam table calculator
http://www.efunda.com/materials/water/steamtable_sat.cfm

i get specific volume of 46.053 kg/m^3 and pressure of 85.698 bars, which i took to be your 86 bars rounded to nearest integer. Note it's absolute pressure.
Since you mentioned cooling through the walls i assumed you meant to use saturated steam.
An enclosure of one cubic meter would contain 46 kg of saturated steam.
Well, 46.053 more exactly.

Were your container 213.75 meters in volume it would contain about 213.75 X 46.053 = ~9844 kg of steam,

were it .006 m^3 it would contain 0.276 kg

Perhaps you'll convert those masses to moles and see how they compare to ideal gas law? Molecular weight of water is 18.015 g/mol.

"a problem well stated is half solved"

 

[pmacias]

To accurately calculate the amount of steam needed to open a relief valve using the ideal gas law, you will need to consider several factors. First, the ideal gas law (PV = nRT) can be used to calculate the amount of steam in a given volume at a specific temperature and pressure. However, this calculation assumes that the steam behaves as an ideal gas, which may not be the case in real-world scenarios.

Additionally, the thermal conductivity and heat loss of the container and its walls will affect the temperature and pressure of the steam inside. This may lead to a decrease in the amount of steam needed to open the relief valve, as the heat loss can cause the steam to condense and reduce in volume.

Furthermore, the pressure at which the relief valve is set to open (86 bars) will also impact the amount of steam needed. If the pressure inside the container exceeds this threshold, the relief valve will open, regardless of the volume of steam present.

In order to accurately determine the amount of steam needed to open the relief valve, it may be necessary to consider other variables such as the flow rate of steam, the size and design of the relief valve, and any other external factors that may affect the system. It may also be helpful to consult with a specialist or refer to industry standards and guidelines for relief valve operation.