Question

An infrared heater has a surface area of 0.06m², and the emissivity of the surface is 0.85. how hot must the surface be for the heater to radiate with a power of 500W

Answer 1

According to Stephen-Boltzmann law:

$$q=\sigma A\epsilon(T_2^4-T_1^4)$$

If the surrounding temperature is 0°C, or 273 K, the temperature of the heater must be

$$T_2=\sqrt[4]{\frac{q}{\sigma A\epsilon}+T_1^4}=650\text{ K},$$

or 377°C.