# Statistical thermodynamics- ideal gases mixture (Reif 3.6)

• sergiopinilla
This is due to the fact that the glass bulb is permeable to helium and not to any other gases. This allows for equilibrium to be reached, resulting in the partial pressure of helium inside the bulb to be equal to the helium pressure outside the bulb. This is known as Dalton's Law of Partial Pressures.

#### sergiopinilla

A glass bulb contains air at room temperature and at a pressure of 1 atmosphere. It is
placed in a chamber ﬁlled with helium gas at 1 atmosphere and at a room temperature. A
few months later, the experimenter happens to read in a journal article that the particular
glass of which the bulb is made is quite permeable to helium, although not to any other
gases. Assuming that equilibrium has been attained by this time, what gas pressure will the
experimenter measure inside the bulb when he goes back to check? Please help, the solutions manual says its 2 atmospheres but I don't really know how to start.

sergiopinilla said:
A glass bulb contains air at room temperature and at a pressure of 1 atmosphere. It is
placed in a chamber ﬁlled with helium gas at 1 atmosphere and at a room temperature. A
few months later, the experimenter happens to read in a journal article that the particular
glass of which the bulb is made is quite permeable to helium, although not to any other
gases. Assuming that equilibrium has been attained by this time, what gas pressure will the
experimenter measure inside the bulb when he goes back to check? Please help, the solutions manual says its 2 atmospheres but I don't really know how to start.

You have to assume that the volume of helium is much, much greater than the volume of the bulb. With a membrane permeable to only helium, what is the relationship between the partial pressure of helium inside the bulb to the helium pressure outside the bulb (ie in the helium chamber surrounding the glass bulb)?

AM

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## 1. What is statistical thermodynamics?

Statistical thermodynamics is a branch of thermodynamics that uses statistical methods to explain the behavior of a large number of particles in a system. It provides a microscopic understanding of thermodynamic properties and allows for the prediction of macroscopic behavior.

## 2. What is an ideal gas mixture?

An ideal gas mixture is a mixture of gases that follows the ideal gas law, which states that the pressure, volume, and temperature of the mixture are related by the equation PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is temperature.

## 3. What is the role of statistical thermodynamics in studying ideal gas mixtures?

Statistical thermodynamics helps to explain the macroscopic behavior of ideal gas mixtures by considering the individual particles and their interactions. It allows for the calculation of thermodynamic properties such as pressure, volume, and entropy of the mixture.

## 4. How are the properties of an ideal gas mixture calculated using statistical thermodynamics?

The properties of an ideal gas mixture can be calculated by using statistical methods such as the Maxwell-Boltzmann distribution and the partition function. These methods take into account the energy levels and interactions of the particles in the mixture to determine the overall behavior of the system.

## 5. What are some real-life applications of statistical thermodynamics in studying ideal gas mixtures?

Statistical thermodynamics is used in various fields such as chemical engineering, materials science, and atmospheric science to study the behavior of gases in mixtures. It is also important in the development of technologies such as refrigeration and air conditioning, where the properties of ideal gas mixtures are crucial. Additionally, it is used to understand and predict the behavior of gases in industrial processes and in the study of Earth's atmosphere.