Calculating pressure in 2-phase closed systems

In summary, the individual is asking for help in calculating the overall pressure in a closed pressure vessel containing water and purged with helium, after heating it to a given temperature. They are unsure which equation of state to use since their system involves both a liquid and a gas. The answer to their question depends on the type of equation of state being used. If it is for a two-phase system, the vapor pressure of water at the desired temperature must be calculated. Otherwise, if it is for a single-phase system, the equation of state can be used directly to calculate the overall pressure.
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I have a closed pressure vessel that is partially filled with water and the head space has been purged with He and charged to about 100 psi. What I wish to know is how to calculate the overall pressure in this vessel after heating it to a given temperature (e.g., 300 or 400 C). I know the volume of water and the head space at ambient temperature.

I think I am having difficulties because I keep wanting to apply an equation of state such as the Redlich-Kwang, BWR, or Soave but these are for gases and in my case I have a liquid and a gas. It is likely that all of the liquid will exist in the vapor state at an end temperature of 400 C but likely it will be a saturated vapor/liquid mix at 300 C.
 
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  • #2
Do I need to calculate the vapor pressure of the water at 300 C or 400 C?The answer to your question depends on what type of equation of state you are using. If you are using an equation of state designed for a two-phase system (gas and liquid in equilibrium), then you would have to calculate the vapor pressure of the water at the desired temperature. However, if you are using an equation of state that is designed for a single-phase system (either gas or liquid) then you would not need to calculate the vapor pressure of the water. In this case, you would simply use the equation of state to calculate the overall pressure in the vessel.
 
  • #3


I would first like to commend you for your careful consideration and use of equations of state in your calculations. However, in this case, as you have correctly identified, the presence of both a liquid and a gas in your closed system makes it more complex than a simple gas-only system.

To accurately calculate the overall pressure in your closed vessel after heating, you will need to use a two-phase equilibrium calculation. This involves considering the vapor and liquid phases separately and then combining their individual pressures to determine the overall pressure. The specific equations and methods used will depend on factors such as the properties of your particular system and the temperature and pressure conditions involved.

One approach to this calculation is to use the Antoine equation, which relates the vapor pressure of a liquid to its temperature. This equation can be used to determine the vapor pressure of the water at your given temperatures of 300 and 400 C. The partial pressure of the helium gas in the head space can also be calculated using the ideal gas law. Then, using Dalton's law of partial pressures, the overall pressure in the vessel can be determined by adding the vapor pressure of the water and the partial pressure of helium.

Alternatively, you could also use a thermodynamic property calculation software or program, which will take into account the properties of both the liquid and gas phases and perform the two-phase equilibrium calculation for you.

In summary, to accurately calculate the overall pressure in your two-phase closed system, you will need to use a two-phase equilibrium calculation, taking into account the properties of both the liquid and gas phases and using appropriate equations or software. I hope this helps guide you in your calculations.
 

1. How is pressure calculated in a 2-phase closed system?

The pressure in a 2-phase closed system can be calculated using the ideal gas law, which states that pressure is equal to the product of the gas's temperature, volume, and the number of moles of gas, divided by the gas constant. In a closed system, the volume and number of moles remain constant, so the pressure can be calculated by simply measuring the temperature of the system and plugging it into the equation.

2. What is a 2-phase closed system?

A 2-phase closed system is a system in which both gas and liquid phases of a substance coexist in a closed container. This usually occurs at a specific temperature and pressure, known as the boiling point, where the substance can exist in both liquid and gas phases.

3. Can pressure in a 2-phase closed system change?

Yes, the pressure in a 2-phase closed system can change if there is a change in temperature or volume. As the temperature increases, more of the substance will turn into gas, leading to an increase in pressure. Similarly, if the volume of the system decreases, the pressure will also increase.

4. How does pressure affect the phases in a closed system?

In a closed system, pressure and temperature are directly related to the phase of a substance. As pressure increases, the boiling point of the substance also increases, leading to a higher likelihood of the substance existing in the liquid phase. On the other hand, decreasing pressure can cause the substance to transition into the gas phase.

5. What factors can affect the accuracy of pressure calculations in a 2-phase closed system?

The accuracy of pressure calculations in a 2-phase closed system can be affected by external factors such as atmospheric pressure, changes in temperature or volume, and the presence of impurities in the system. It is important to ensure that these factors are controlled and accounted for in order to obtain accurate pressure measurements.

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