Bose condense an initially classic gas

[Odyssey]

Homework Statement

Consider a gas of 10^6 bosonic atoms at fixed temperature. Can you make an initially classical gas Bose condense by only changing the volume keeping the temperature fixed? Why?

Homework Equations

condensation temperature of a free Bose gas equation: T = 0.527(h^2/2*Pi*m)(N/V)^(2/3)

The Attempt at a Solution

This is the only equation I have found that could be helpful. Here is my logic...since that equation only depends on V and not T...the answer is yes...? Sorry...really stuck here.

 

[anathema]

Thank you for your question. The answer to your question is yes, you can indeed make an initially classical gas Bose condense by only changing the volume while keeping the temperature fixed. This is because the condensation temperature of a free Bose gas is solely dependent on the number of particles (N) and the volume (V), as shown in the equation you provided. This means that by changing the volume of the gas, you can manipulate the number of particles in the gas, and therefore, the condensation temperature.

In the case of a fixed temperature, increasing the volume would decrease the number of particles per unit volume (N/V), which in turn would decrease the condensation temperature. At a certain volume, the number of particles per unit volume would reach a critical value, and the condensation temperature would drop to the temperature of the gas. This is known as Bose-Einstein condensation.

In summary, by changing the volume while keeping the temperature fixed, you can indeed make an initially classical gas Bose condense. I hope this helps clarify your question. Please let me know if you have any further questions.

 

[nlightner]

I would like to clarify that Bose-Einstein condensation is a phenomenon that occurs at very low temperatures, typically close to absolute zero. Therefore, the temperature of the gas mentioned in the homework statement is most likely not low enough to undergo Bose-Einstein condensation.

However, if we assume that the temperature is low enough for condensation to occur, then yes, it is possible to make an initially classical gas undergo Bose-Einstein condensation by changing the volume while keeping the temperature fixed. This is because the condensation temperature of a free Bose gas, as given by the equation provided, depends only on the volume and not the temperature.

This can be explained by considering the behavior of the gas particles. In a classical gas, the particles have enough kinetic energy to move freely and do not interact with each other significantly. However, as the volume is decreased, the particles come closer together and their interactions become more significant. At a certain volume, the interactions between the particles become strong enough to cause the gas to undergo a phase transition and form a Bose-Einstein condensate.

Therefore, by decreasing the volume, we are increasing the density of the gas and promoting the formation of a Bose-Einstein condensate. Keeping the temperature fixed ensures that the particles do not gain any extra energy and remain in their lowest energy state, which is necessary for Bose-Einstein condensation to occur.

In summary, it is possible to make an initially classical gas undergo Bose-Einstein condensation by changing the volume while keeping the temperature fixed, as long as the temperature is low enough for condensation to occur.