Question

The specturm of a black body at two temperatures `27^(@)C` and `327^(@)C` is show in the Fig. `7(e).20`. Let `A_(1)` and `A_(2)` be the respective areas tunder the two curved. Estimate the ratio `A_(2)//A_(1)`.

Answer 1

Correct Answer - `[16 : 1]`
Here, `T_(1)= 27^(@)C= 27+273=300 K`,
`T_(2)=327^(@)C=327+273=600 K`.
Area (A) under the intensity - wavelength curve measures the amount of thermal energy (E) radiatied per second per unit area from a black body, i.e.,
`(A_(2))/(A_(1))=(E_(2))/(E_(1))=(sigmaT_(2)^(4))/(sigma T_(1)^(4))=((T_(2))/(T_(1)))^(4) = ((600)/(300))^(4) =2^(4) =16`