Textbook 4G.1 (B)

[106046096]

Hi! I know you would use the Boltzmann equation to solve, but I am confused about how you would find variable W for the equation. Can someone explain please? Thanke you!

[405972194]

I believe W is the number of orientations to the power of the number of molecules

So for your example since there are 64 molecules and part B states that the molecules have four orientations, W = 4^64

[MafruhaR]

The Boltzmann equation is a fundamental equation in statistical mechanics that describes the behavior of particles in a gas. It relates the distribution of particle velocities to the temperature and mass of the particles, among other parameters. The variable W in the Boltzmann equation represents the velocity distribution function. This function gives the probability density of finding a particle with a specific velocity at a given point in [censored]

[Avantika MOhan_2B]

Hi! The variable W is defined as the orientations of the particles in the compound^ number of particles in the compound. So for a compound with 64 molecules, the number of particles = 64. So we have W = x^64 for whatever x might be. W, here, refers to the different possible states the compound can exist as determined by the orientations of the particles in it. Part A) asks us: all aligned in the same direction. In order for all the particles in the compound to be aligned in the same direction the only possible orientation is facing one way. All the particles face left OR right they can't face left and right. So we have S = Kbln(W) WHERE W = 1^64 or just 1. For part 2) the question says they lie in any four orientations with the same energy. SO we have four orientations - say left, right, up and down - and they're arranged in these orientations for 64 particles. The number of possible states is 4^64. So S = Kbln(W) = Kb*ln(4^64). Hope this helped!