Radiation

Blackbody Radiation

All matter emits electromagnetic radiation…

However, treated as a surface phenomenon, radiation can transmit through vacuums without a medium needed

For an idealized blackbody radiation,
$Q_{\max }^{\prime }=\sigma T^4$

1. A blackbody emits maximum radiation for a given temperature
2. It serves as an ideal standard for comparing real surfaces
3. It is a perfect emitter
4. It absorbs all incident radiation

Kirchoffs Law of Thermal Radiation

Requires thermodynamic equilibrium between source and surroundings
Can be used, but proceed with caution when |T_s-T_surr| > 100K $ϵ=\alpha$

both values are between 0 and 1.

$Q_{net}^{\prime }=ϵ\sigma T_s^4-\alpha \sigma T_{surr}^4$
Where epsilon = alpha in specific cases so…
$Q_{net}^{\prime }=\sigma ϵ\left(T_s^2+T_{surr}^2\right)\left(T_s+T_{surr}\right)\left(T_s+T_{surr}\right)\left(T_s-T_{surr}\right)$
$Q_{net}^{\prime }=h_{rad}\left(Ts,T_{surr}\right)\left(T_s-T_{surr}\right)$ So h_rad is…
$h_{rad}=ϵ\sigma \left(T_s^2+T_{surr}^2\right)\left(T_s+T_{surr}\right)$
Emitted radiation varies continuously with wavelength where emitted radiation increases as temperature rises.

$E_b\left(T\right)={\int }_0^{\infty }{E}_{b\lambda }\left(\lambda ,T\right)d\lambda =\sigma T^4$

Absorptivity, Reflectivity, Transmissivity

Absorptivity $\alpha ={\frac{ra{d}_{absorbed}}{ra{d}_{incident}}}_{}$
Reflectivity $\rho ={\frac{ra{d}_{reflected}}{ra{d}_{incident}}}_{}$ Transmissivity $\tau =\frac{ra{d}_{transmitted}}{ra{d}_{incident}}$

Intro to Radiation

Equations
$Q_{\max }^{\prime }=\sigma T_s^4$
$Q_{emit}^{\prime }=ϵ\sigma T_s^4$
$Q_{emit}^{\prime }=\alpha \sigma T_{surr}^4$
*The main radiation equation
$Q_{rad}^{\prime }=h_{rad}\left(T_s^{}-T_{surr}\right)=ϵ\sigma \left(T_s^4-T_{surr}^4\right)$