Answer to Question #90103 in Mechanics | Relativity for Awesome

Question

Calculate the maximum monochromatic emissive power at 288k

Answer 1

Wien’s Displacement Law:

$$E_{\lambda}=\frac{C_1\lambda^{-5}}{exp^{\frac{C_2}{\lambda T}}-1}$$

the wavelength at which emissive power is maximum:

$$\lambda_{max}=\frac{C_2}{4.965\times T}=\frac{0.0029}{T} m$$

If we substitute this wavelength in the Wien's Displacement law, then the magnitude of the maximum monochromatic emissive power is

$$E_{max}=1.285\times 10^{-5}\times T^5=\\ 1.285\times 10^{-5}\times 288^5 = 25.46\times 10^6 \frac{W}{m^2}$$