- #1

Hypatio

- 151

- 1

I am reading the text 'thermal radiation heat transfer' by Howell et al. (2011). In it they describe normal spectral emission by an isothermal volume element dV as

[itex]4\pi \kappa_\lambda I_{\lambda b}(S)dVd\lambda[/itex]

where [itex]\kappa_{\lambda}[/itex] is the absorption coefficient and [itex]I_{\lambda b}[/itex] is the black body spectrum, V is volume, and [itex]\lambda[/itex] is the wavelength.

And later state that if the refractive index [itex]n[/itex] is not equal to 1, it should be included as

[itex]n_{\lambda}^2(S)\kappa_\lambda(S)I_{\lambda b}(S)dS[/itex]

Much earlier they define

[itex]I_{\lambda b}=\frac{2\pi h c^2}{n^2\lambda^5\left[\exp\left(\frac{hc}{nk_B\lambda T}\right)-1\right]}[/itex]

It seems that this must mean that

[itex]4\pi \kappa_\lambda \frac{2\pi h c^2}{\lambda^5\left[\exp\left(\frac{hc}{nk_B\lambda T}\right)-1\right]}(S)dVd\lambda[/itex]

is the correct form for calculating spectral power.

However, the authors continually jump around with and without the use of the index of refraction and I don't know what the correct form of [itex]I_{\lambda b}[/itex] is. This jumping around with definitions is all very confusing. So what is the correct form of the first equation? What is the actual dependnece of refractive index on emitted power?

Also, I have no idea why emission (a sub-atomic or atomic phenomenon) depends on the the index of refraction (an interatomic medium property).

Also, does this dependence on refractive index only occur in emission or does it also impact absorption? The authors always only talk about emission when referring to the dependence on the index of refraction.

[itex]4\pi \kappa_\lambda I_{\lambda b}(S)dVd\lambda[/itex]

where [itex]\kappa_{\lambda}[/itex] is the absorption coefficient and [itex]I_{\lambda b}[/itex] is the black body spectrum, V is volume, and [itex]\lambda[/itex] is the wavelength.

And later state that if the refractive index [itex]n[/itex] is not equal to 1, it should be included as

[itex]n_{\lambda}^2(S)\kappa_\lambda(S)I_{\lambda b}(S)dS[/itex]

Much earlier they define

[itex]I_{\lambda b}=\frac{2\pi h c^2}{n^2\lambda^5\left[\exp\left(\frac{hc}{nk_B\lambda T}\right)-1\right]}[/itex]

It seems that this must mean that

[itex]4\pi \kappa_\lambda \frac{2\pi h c^2}{\lambda^5\left[\exp\left(\frac{hc}{nk_B\lambda T}\right)-1\right]}(S)dVd\lambda[/itex]

is the correct form for calculating spectral power.

However, the authors continually jump around with and without the use of the index of refraction and I don't know what the correct form of [itex]I_{\lambda b}[/itex] is. This jumping around with definitions is all very confusing. So what is the correct form of the first equation? What is the actual dependnece of refractive index on emitted power?

Also, I have no idea why emission (a sub-atomic or atomic phenomenon) depends on the the index of refraction (an interatomic medium property).

Also, does this dependence on refractive index only occur in emission or does it also impact absorption? The authors always only talk about emission when referring to the dependence on the index of refraction.

Last edited: