How Does Introducing Gas into a Torus Affect Vapour Pressure?

[tirrel]

Hi... I found this site a lot time ago and sometimes I feel like viewing your problems, maybe in a future I'll be active... I want to say that this IS NOT an homework, but it's an exercise I was never able to solve and so I try to put it here, even if I don't know whether it is the right section of the forum...

Homework Statement

I'll try to describe a picture.

This is the situation. Imagine a thorus half-filled with a liquid. At the beginning of course the water will fill the lower part of the torus (part A) and the other part (part B) will be filled with its vapour. Now dived part B using a membrane pouros with respect to the vapour. This membrane at this moment doesn't have physical effects, but it divides part B of the thorus into part B1 and B2.

Now we take a gas which the membrane doen't let pass and pump it at pressure P into part B1 of the thorus.

Data: density of the liquid: $n_L$, density of the vapour $n_v$.

Question: how much has changed the vapour pressure from its initial value?

Homework Equations

boh...law of perfect gases?, chemical potentials?, work done by the gas pumped?...

The Attempt at a Solution

Actually I don't have serious attempts to propose... it's years that I haven't got a solution to this problem...

 

[AvroArrow]

I tried to work using the law of perfect gases but it did not work and now I'm stuck. I would like to find a way to solve this problem... Thanks in advance.

 

[thomate1]

As a scientist, it is important to first understand the problem and gather all relevant information before attempting to solve it. From the given information, it seems that the problem involves changes in vapour pressure due to the introduction of a gas into one part of a torus filled with liquid and vapour. Some important factors to consider in this scenario are the properties of the liquid and vapour, the effects of the membrane, and the pressure and density of the gas being introduced.

To solve this problem, one could use the ideal gas law to calculate the change in vapour pressure. However, this may not be accurate as the gas being introduced may not behave as an ideal gas. Another approach could be to use chemical potentials to determine the change in vapour pressure. This would involve considering the interactions between the liquid, vapour, and gas, as well as the work done by the gas as it is pumped into the thorus.

It is also important to consider the physical effects of the membrane on the system. How does it affect the distribution of the liquid and vapour in the thorus? Does it have any impact on the pressure or density of the gas being introduced? These are all important factors to consider when attempting to solve this problem.

In conclusion, this problem requires a thorough understanding of the properties of the system and the interactions between its components. It may also require the use of multiple equations and approaches to accurately determine the change in vapour pressure. As a scientist, it is important to approach problems with a critical and analytical mindset, and to continue exploring different solutions until a satisfactory answer is found.