Recent content by raghav

Homework Statement Find the volume enclosed between the by the cylinder x^2 + y^2 = 2ax and z^{2} = 2ax Homework Equations The Attempt at a Solution The problem can be done by evaluating the triple integral \int \int \int dxdydz , but i am not able to visualise how the second...

Yes I have indeed given all the necessary details the problem demands. Essentially my doubt boils down to evaluating the integral \int_{0}^{a} \frac{t^{3}}{e^{t}-1}dt ; a being some constant.

exactly. Or to be more explicit on the above result, \mathrm{div}\vec{u} = \frac{\oint_{S} \vec{u}\cdot \vec{dS}}{V} . In fact we can derive this using the mean value theorem on integrals on the divergence theorem. :smile:

Yes i could evaluate the denominator using the standard integral u have mentioned, however the Numerator is creating trouble. I have also tried a parts argument, doesn't seem to be taking me any where :cry: Some1 please help asap

Homework Statement In case of Cavity Radiation(Blackbody radiation) let \rho_{T}(\nu)d\nu denote the energy density of radiation having frequency in the interval \nu and \nu + d\nu. Then we need to show that \frac{\int_{0}^{\lambda_{max}} \rho_{T}(\nu)d\nu}{\int_{0}^{\infty}...

Hence it means that R_{T}(\nu}d\nu is the power absorbed, per unit area by radiation with frequency lying in \nu and \nu + d\nu . But I don't quite get the physical interpretation of the result. Do you mind throwing some light on that sir?

oh ok sir

I fail to understand why that sentence of mine is appearing latexified :frown:

hmm yes sir I did that, and got something like this: \frac{8(kT)^{4}\pi^{5}}{(hc)^{3}\cdot 15} Ok so now in order that i prove my problem All i do is to divide Stefan's Law by the above right? keeping of course in mind stefans constant in terms of h, c , k. Is the relation true only...

Since the latter quantity denotes energy density, the integral over all frequencies should give us total radiant energy contained in the cavity, which is kT if we assume that T is the absolute temperatre of the cavity. Am I right sir?

Can someone please help me out with this one? Thanks in advance.

Spectral Radiancy R(\nu) is defined such that R_{T}(\nu)d\nu gives the energy absorbed per unit area per unit time when radiation has frequency between \nu and \nu + d\nu. It is essentially power

Homework Statement Suppose that a blackbody spectrum is specified by Spectral Radiancy R_{T} (\nu) d\nu and Energy Density \rho_{T} (\nu) d\nu then show that R_{T} (\nu) d\nu = \frac {c}{4}\cdot \rho_{T} (\nu) d\nu Homework Equations \rho_{T} (\nu) d\nu = \frac{8 \pi h \nu^{3}...