# Does this violate Stefan's law

Radiation energy per unit time is given Stefan-Boltzmann law as being proportional to temperature to the 4th power, and to surface area of the body. (For black bodies) This was told to me in our physics lecture. Later for a non black body it is the same except being multiplied by another constant called the emissivity of the body I am told emissivity is the ratio of the radiant energy emitted by a black body in unit time to the energy emitted by the body in hand. This makes perfect sense till the time I am told that:

Emissivity of the body depends on temperature of the body. This can only give 2 conclusions: Either radiant energy emitted per unit time is not proportional to temperature to the 4th power or, Regular bodies do not emit energy like blackbodies. If this is true, is there an alternate more accurate radiation heat transfer models for regular bodies, what are they? Also tell me which conclusion is correct?

• While there are thermochromes that have variable emissivity, for most materials that effect is negligible. Where did you read the statement about the temperature dependent emissivity? Could it be that something got lost in translation? – CuriousOne Dec 27 '14 at 16:13
• @Sashurocks Stefan's law ($\propto T^4$) only applies for ideal black body radiation. So if the emissivity really depends on temperature, which I'm not sure, then for regular bodies it would not be proportional to $T^4$ – M. Zeng Dec 27 '14 at 16:22
• I think it is no surprise that the property of a body depend on its state, and so by its temperature say. The sense of this is that, by increasing the temperature you also increase the kinetic energy of the particle making up your body, so you can argue that your body emits differently at different temperatures. Heuristically you can then assume that emissivity $\epsilon$ is a function $\epsilon(T)$. Usually this dependence is quite weak so as customary you can perform a Maclauring expansion and retain the first few orders, $\epsilon(T) = \epsilon_0+\alpha T + \beta T^2 + \cdots$. – Phoenix87 Dec 27 '14 at 16:28
• @curiousone , they mentioned emissivity of regular materials at specific temperatures, like that of oxidised iron at 200F and so, due to which I got this doubt. – Sashurocks Dec 27 '14 at 16:36
• @Sashurocks: Can you give a link to the emissivity data? – CuriousOne Dec 27 '14 at 16:38