# [Thermodynamics] How much mass is extracted to decrease pressure

• wasmaro
In summary, when pressure decreases, the mass of a substance also decreases due to the inverse relationship between pressure and mass according to the ideal gas law. The amount of mass extracted depends on the specific substance and change in pressure, and it is possible to decrease pressure without extracting any mass if the volume of the system increases while the mass remains constant. The type of substance also affects the amount of mass extracted, as different substances have different molecular weights and densities. However, the extraction of mass by decreasing pressure can be reversed by either increasing the pressure back to its original level or reintroducing the extracted mass into the system.
wasmaro
Homework Statement
I have a pressurized cold vessel with a saturated liquid and saturated vapor. Due slow heat transfer, the vessel increases in pressure and needs to be relieved. I want to estimate the mass of vapor that needs to be extracted in order to depressurize the vessel to a desired value.

I know the initial pressure (P1) and temperature (T1), I know the desired pressure (P2), the vessel geometry and liquid volume. I'm assuming no heat transfer as the mass extraction process will be quick.

Any idea how to approach this problem?
Relevant Equations
First Law of Thermodynamics
I have a feeling some integration will be required, I just want to see if anyone know of a quick way.

## 1. How does decreasing pressure affect mass extraction in thermodynamics?

In thermodynamics, decreasing pressure can lead to a decrease in the amount of mass extracted. This is because as pressure decreases, the molecules in a substance have more space to move around, making it more difficult to extract a large amount of mass.

## 2. Is there a specific formula to calculate the amount of mass extracted when pressure is decreased?

Yes, there is a formula known as the Gibbs-Duhem equation that can be used to calculate the change in mass when pressure is decreased. This equation takes into account factors such as temperature, volume, and the number of moles of a substance.

## 3. Can mass extraction be used to control pressure in a system?

Yes, mass extraction can be used as a method to control pressure in a system. By removing a certain amount of mass, the pressure in the system can be lowered. This is commonly seen in refrigeration systems, where the removal of mass (such as water vapor) helps to decrease the pressure and lower the temperature.

## 4. How does the type of substance being extracted affect the amount of mass that can be extracted?

The type of substance being extracted can have a significant impact on the amount of mass that can be extracted. For example, gases are much easier to extract than liquids or solids, as their molecules have more space to move around. Additionally, the properties of the substance (such as its boiling point and vapor pressure) can also affect the amount of mass that can be extracted.

## 5. Are there any limitations to mass extraction in decreasing pressure?

Yes, there are limitations to mass extraction in decreasing pressure. The amount of mass that can be extracted is limited by the properties of the substance and the conditions of the system. Additionally, the process of mass extraction can also be energy-intensive and may not be feasible in all situations.

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