Q: Three disc A, B and C having radii 2 m, 4 m and 6 m respectively are coated with carbon black on their outer surfaces. The wavelengths corresponding to maximum intensity are 3000 nm, 4000 nm and 5000 nm respectively. The power radiated by them are QA , QB and QC respectively.
(a) QA is maximum
(b) QB is maximum
(c) QC is maximum
(d) QA = QB = QC
Ans:(b)
Sol: As Q ∝ AT4 and λm T= constant.
$ \displaystyle Q \propto \frac{A}{(\lambda_m)^4} $
$ \displaystyle Q \propto \frac{r^2}{(\lambda_m)^4} $
$ \displaystyle Q_A : Q_B : Q_C = \frac{2^2}{3^4} : \frac{4^2}{4^4} : \frac{6^2}{5^4} $
$ \displaystyle Q_A : Q_B : Q_C = \frac{4}{81} : \frac{1}{16} : \frac{36}{625} $
i.e., QB is maximum.