0
votes
0answers
24 views

Thermal Conduction through sphere

In general, a sphere with conductivity $\kappa$, heat capacity per unit volume $C$ and radius $R$ obeys the differential equation at time t: $$C\frac{\partial T}{\partial t} = \kappa \frac{\partial^2 ...
3
votes
2answers
120 views

Why don't the derivatives of the blackbody spectrum over frequency and wavelength match?

The question is: The radiation emitted by a black body can be represented either by the energy distribution over the wavelength or by that over the frequency. In the first case the maximum energy ...
1
vote
0answers
158 views

Radiative cooling time for a black body

Okay, so this is confusing me a bit. How can I calculate the time it takes to cool a perfect black body from an initial temperature $T$ down to equilibrium temperature (say, 3 K for space)? I know ...
0
votes
1answer
146 views

Filament in a lightbulb, thermal radiation

I'm trying the following: The filament inside a 100 W lightbulb has an absorption coefficient of 0.25, and while operating, it is at a temperature of 2,573 K. What's the size of the surface of the ...
4
votes
1answer
776 views

Wien's displacement law in frequency domain [duplicate]

When I tried to derive the Wien's displacement law I used Planck's law for blackbody radiation: $I_\nu = \frac{8 \pi \nu^2}{c^3} \frac{h \nu}{e^{h\nu/k_bT}-1}$ Asking for maximum: $\frac{dI_\nu}{d ...
2
votes
2answers
300 views

Showing Wien's Displacement Law from Wien's Law

Does anyone know how I would show that $\lambda * T$ is constant, using only Wien's Law? That $\rho(\lambda,T) = 1/\lambda^5*f(\lambda T)$ I differentiated, but all I could get was $\lambda T = ...
1
vote
2answers
89 views

Photon gas kinetic theory

Suppose a black body as an enclosure of volume $V$ with a hole of section $A$. In the interior there is a photon gas, whose energy density $u$ is, at temperature $T$. $$ u=cT^4$$ How can I show that ...
1
vote
1answer
1k views

Find temperature of surface (Blackbody Radiation) [closed]

An astronomer is trying to estimate the surface temperature of a star with a radius of $5 \times 10^8\ m$ by modeling it as an ideal blackbody. The astronomer has measured the intensity of ...
1
vote
1answer
1k views

Calculating the amount of heat energy radiated by sun

How do I calaculate the amount of heat energy radiated from the sun in one minute?? Well, i tried some stefan method, but the answer seems far off from the correct one....well, i would thus strongly ...
3
votes
2answers
1k views

Are Newton's law of Cooling and Stefan's law related?

Many of Indian school textbooks claim a proof of Newton's law of cooling from Stefan's law of black-body radiation. As far as I am aware of, Newton's law is based on cooling from convection currents ...
1
vote
2answers
1k views

Calculate temperature of the earth through blackbody radiation

I don't understand the solutions to a problem about blackbody radiation and was wondering if anybody could help me out. Here is the question: The sun can be considered as a blackbody radiation ...
0
votes
1answer
229 views

Mathematical derivation of $N(\lambda)d\lambda$

We all know that in Rayleigh-Jeans law, $$N(f)df ~=~ 8\pi f^2 df/c^3.$$ How do you derive $N(\lambda)d\lambda$? I am sort of confused...
-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 ...
1
vote
1answer
203 views

2d or 1d conduction in this scenario?

There is a rectangular fin attached to a heat exchanger with a base temperature of 350K. The fin has uniform properties and experiencesa uniform heat generation. It also experiences heat transfer with ...