Answer to Question #115299 in Optics for Vidurjah Perananthan

Question

A human body has a surface temperature of about 33 ° C and can be considered a black body. a) Calculate at what wavelength the human body has its radiation maximum.
b) Imagine that you are in a room with a certain temperature. What net effect (radiated power minus absorbed power) radiates your body? Make appropriate estimates. (Suppose your body is a black body and it absorbs radiation from all wavelengths)

Answer 1

a) We can use Wien's displacement law:

$$\lambda=\frac{b}{T}=\frac{2.898×10^{−3}}{33+273}=9.47\cdot10^{-6}\text{ m}.$$

b) The rate of heat transfer can be expressed as

$$\frac{Q_\text{net}}{t}=\sigma eA(T_2^2-T_1^2),$$

where

e - emissivity of skin in the infrared 0.97),

A - surface area of our body.