Recent content by SirCrayon

Homework Statement Consider the distribution function F(x) = Cexp(-ax) Find the normalization constant C Homework Equations The Attempt at a Solution This is more clarification since this is not actually a homework problem but was in my profs notes. He started with the...

Homework Statement Ideal gas. In an ideal-gas model. N molecules move almost indepdently with very weak interactions between, in a three-dimensional box of volume V. Find the heat capacity of the system. SHO. Consider N independent SHOs in a system. each osciallating about a fixed point...

I can't seem to find the sign that's wrong, the only thing that I can reduce is the (KT/mg)^2 right? I can't figure out how to cancel anything else. Setting h=0 should give me the term i need and same with inifinity for c). Thanks. But i can't seem to figure out the above

Yes I have, <z> = ∫ z f(z) dz / ∫ f(z) dz = ∫ z exp(-mgz/(kT)) dz / ∫ exp(-mgz/(kT)) dz = (kT)^2/(mg)^2 * (e^(-mgh/kT)*(-mgh/kT - 1) - 1)) / -(kT/mg)[(e-mg/h/KT)-1]

Yes sorry, all the z's in a,b,c are z¯

Thanks, I think i have figured out a) with the below: <z> = ∫ z f(z) dz / ∫ f(z) dz = ∫ z exp(-mgz/(kT)) dz / ∫ exp(-mgz/(kT)) dz where the integrations are from z = 0 to z = h. I am pretty stumped on b and c though

Homework Statement Let a box of height h be filled with classical ideal gas molecules of mass m in a constant gravitational filed g. As will be shown later, the distribution molecular height z obeys: f(z) = C exp (-mgz/KT) Where C is the normalization constant a) find the average height...