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

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Discussion Overview

The discussion revolves around determining the amount of steam required to open a relief valve using the ideal gas law and steam tables. Participants explore the implications of using ideal gas assumptions versus real gas behavior, particularly in the context of steam at high temperatures and pressures.

Discussion Character

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

Main Points Raised

  • One participant expresses uncertainty about using the ideal gas law to calculate the amount of steam needed to open a relief valve, questioning whether the calculated volume corresponds to the valve's opening point.
  • Another participant points out that saturated steam does not behave as an ideal gas and suggests using steam tables to find the specific volume at the given temperature and pressure.
  • A participant proposes a method for using steam tables, questioning how to interpret the specific volume in relation to their container's volume and whether the real gas law, which accounts for compressibility, should be applied.
  • One participant clarifies that specific volume is the inverse of density and provides specific volume data for saturated steam at the stated temperature and pressure, calculating the mass of steam in various container volumes.
  • There is a suggestion to convert the calculated masses of steam to moles for comparison with the ideal gas law, noting the molecular weight of water.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the appropriate approach to use for calculating the steam volume needed to open the relief valve. There are competing views on whether to use the ideal gas law or steam tables, and uncertainty remains regarding the implications of steam behavior under the given conditions.

Contextual Notes

Limitations include the assumption that steam behaves ideally, the dependence on accurate temperature and pressure readings, and the potential impact of heat loss through the container walls, which may not be fully accounted for in the calculations.

bionic6manuel
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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
 
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saturated steam is not ideal gas.

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

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