MHT CET202615 April 2026Morning ShiftPhysicsThermal Properties of MatterActual
A black disc has a radius 'R' and wavelength corresponding to the maximum intensity is ' '. The emissive power (E) for the different radii and maximum wavelengths is directly proportional to
Options
- AR,
- BR^2, ⁻⁴
- CR^2, ⁻²
- DR^2,
Correct answer
B. R^2, ⁻⁴
Step-by-step solution
The total emissive power of a black body is given by the Stefan-Boltzmann law: E = A T^4 For a disc of radius R , the surface area A R^2 . Therefore, the emissive power is proportional to: E R^2 T^4 According to Wien's displacement law, the wavelength corresponding to maximum intensity is related to the absolute temperature T as: T = b T ⁻¹ Substituting this into the proportionality for E , we get: E R^2 ( ⁻¹)^4 E R^2 ⁻⁴ Answer: R^2, ⁻⁴