1
vote
0answers
16 views

Effusion of particles from one box to another - pressure calculation

Suppose we have a container divided into equal halves. Right half is fixed at temperature $T$, volume $\frac{V}{2}$. Initially it has pressure $P_0$, a hole of area $A$ is opened between them. I ...
0
votes
1answer
41 views

Entropy and chemical potential of an ideal gas

I am reading Schroeder's book "Thermal Physics". One calculation in the text was not quite clear to me. The entropy of an ideal gas is given by the Sackur-Tetrode equation: $$ ...
6
votes
2answers
63 views

Classical and Semi-classical treatments of the ideal gas

In the semi-classical treatment of the ideal gas, we write the partition function for the system as $$Z = \frac{Z(1)^N}{N!}$$ where $Z(1)$ is the single particle partition function and $N$ is the ...
1
vote
1answer
142 views

Understanding collision terms in Boltzmann equation

I am reading a paper that deals with the Boltzmann equation. They add a collision which is supposed to account for collisions which happen when particles are within a radius of $d$ from each other. ...
0
votes
1answer
68 views

How do we know that the Virial Expansion exists?

How do we know that the Virial Expansion exists? How do we know that we may always write $\frac{p}{kT}$ as a power series in $\frac{N}{V}$? That is, how do we know that there exists $B_{i}$ so that ...
3
votes
5answers
448 views

Does it take infinite energy to create a perfect vacuum?

Question is inspired by a recent burst of perpetuum mobile-type questions. It would be nice if one could simply discard them all by an argument that shows it's impossible to create a perfect vacuum. ...
0
votes
1answer
116 views

“Pressure - Average Energy” ratio of ideal quantum gas?

Classically, one can easily show the following relation using a straightforward canonical ensemble computation for a non-interacting gas: $$\frac{PV}{\langle E\rangle}=\frac{2}{3}$$ Now, apparently ...
5
votes
3answers
196 views

Physical intuition for independence of components of velocity in derivation of Maxwell–Boltzmann distribution

Maxwell derived the shape of the probability distribution of velocity of gas particles by starting with just two assumptions. These are: The probability distribution is rotation invariant. The ...
1
vote
2answers
397 views

Why doesnt this violate 2nd law of thermodynamics?

Consider an ideal gas in a cylindrical container in a gravitational field, with a piston on top pushing down by gravity. The piston has some locking mechanism that locks it in place if it is displaced ...
1
vote
1answer
250 views

Rate of effusion in kinetic molecular theory?

According to the kinetic molecular theory obeying Maxwell-Boltzmann distribution of speeds, the rate of effusion through a pinhole of area $A$ is $$R=\frac{PA}{\sqrt{2\pi M R T}}$$ where $M$ is the ...
2
votes
0answers
59 views

error propagation and collision in ideal gas

When dealing with gas, a statistical approach is needed because For N particles, you have to solve 6N equations which cant be done analytically. To know our time step for numerical solving, you can ...
3
votes
2answers
446 views

Canonical partition of a boson gas

I have a 1D gas made of $N$ particles placed in a harmonic potential well, so the Hamiltonian is: $$ \mathcal H = \sum_{j=1}^N \left ( \frac{p_j^2}{2m} + \frac{1}{2}m\omega^2 x_j^2 \right )$$ The ...
1
vote
1answer
363 views

Velocity of real gas molecules?

It is known that the velocity of ideal gas molecules can be computed using Maxwell-Boltzmann law of distribution of molecular velocities, with average velocity given as: ...
1
vote
2answers
134 views

Is it possible to find the number of gas atoms/molecules in a box when the number is small?

Given very low number of particles in a system (e.g. in the 100s), is there a way to accurately measure the number of particles in the system? Assume temperature, pressure and volume is constant and ...
5
votes
1answer
266 views

Ideal gas and diatomic gas with same temperature

If a box of ideal gas and another box of diatomic gas are in thermal equilibrium, does it mean that the average translational energy of ideal gas particle (A) is the same as that of diatomic gas ...
2
votes
2answers
141 views

May molecules of ideal gases have an inner structure?

The following question is probably very elementary: whether molecules of ideal gases may have optic properties? As far as I understand, when one discusses optic properties, one assumes that molecules ...
-1
votes
1answer
243 views

Black body balloon in vacuum [closed]

The problem statement, all variables and given/known data There is a perfectly spherical balloon with surface painted black. It is placed in a perfect vacuum. It is gently inflated with an ideal ...