weins law help

Question

According to Wien's Law, how many times hotter is an object whose blackbody emission spectrum peaks in the blue, at a wave length of 450 nm, than a object whose spectrum peaks in the red, at 700 nm? Please show me your calculations.

Answer 1

Let T = absolute temperature of the body

 

Wein's law states

 

λ_maxT = c, where c is a constant and λ_max = wavelength of peak emission

 

For one body, λ_max1 = 450 nm, for the other it is λ_max2 = 700 nm.  Take the ratio of λ_maxT for both bodies and you will get a relation between their absolute temperatures:

 

(λ_max1T₁₎ / (λ_max2T₂) = c/c = 1

 

Then

 

(450 nm * T₁) / (700 nm * T₂) = 1 ⇒ T₁ = (700 / 450) T₂ = 1.556 T₂

 

This means that body 1 is 1.556 times as hot as body 2.  Therefore the body with peak emission at 450 nm is 1.556 times as hot as the body with peak emission at 700 nm.