Question

Using Wien’s Law, estimate the wavelength at which these common materials radiate their peak brightness (show your work):

walls at 300 K:

ice water at 273 K :

hot water at 373 K :

skin at 310 K:

An incandescent light bulb at 3000 K

Answer 1

Explanation:

Wien’s Law:

$\lambda _{max}\propto \frac{1}{temperature}$

The law states that the wavelength at which black body emits maximum heat  is inversely proportional to the temperature of the body in Kelvins.

$\lambda _{max}=\frac{2.9\times 10^{-3}}{T}$

1) Walls at 300 K

$\lambda _{max}=\frac{2.9\times 10^{-3} mK}{300 K}$

$\lambda _{max}=9.666\times 10^{-6} m$

2) Ice water at 273 K :

$\lambda _{max}=\frac{2.9\times 10^{-3} mK}{273 K}$

$\lambda _{max}=1.062\times 10^{-5} m$

3) Hot water at 373 K :

$\lambda _{max}=\frac{2.9\times 10^{-3} mK}{373 K}$

$\lambda _{max}=7.775\times 10^{-6} m$

4)Skin at 310 K:

$\lambda _{max}=\frac{2.9\times 10^{-3} mK}{310 K}$

$\lambda _{max}=9.355\times 10^{-6} m$

5)An incandescent light bulb at 3000 K

$\lambda _{max}=\frac{2.9\times 10^{-3} mK}{3000 K}$

$\lambda _{max}=9.666\times 10^{-7} m$