11.3 Radiation by Kar Hong

Stefan-Boltzmann Equation

karhonglk2015 — 2015-09-17 10:04:02 UTC

To calculate total energy emmited per second

$$ \frac{dQ}{dt} = P = e\sigma AT^4 $$

Q = heat energy (J)

t = time

P = power (W)

e = emissivity of surface (no unit)

$$= 5.67 * 10^-8 Wm^{-2} K^{-4}$$

A = surface area (m^2)

T = absolute temperature (K)

karhonglk2015 — 2015-09-17 10:16:54 UTC

-no unit

- $$0\leq e \leq 1$$

Shiny object with smooth surface → Poor radiator → value of e is low

Dark object with rough surface → Good radiator → value of e is high

karhonglk2015 — 2015-09-17 11:00:02 UTC

- At the same time an object is radiating heat, it also absorb heat from surrounding

-Good radiator = Good absorber

-Bad radiator = Bad absorber

-Net heat radiated by object is difference between heat emitted by object and heat absorbed by object.

$$ Q_{net} = Q_{emit} - Q_{absorb} $$

-Therefore, net power can be calculated by

$$ P_{net} = e\sigma A(T^4_0 - T^4_s)$$

T_0=Absolute temperature of object

T_s =Absolute temperature of surrounding