Two blackbody spectral-intensity-versus-wavelength curves A and B have total areas in the ratio 16:1, with A the higher-intensity curve. The temperature for B is 27°C. If the temperature for A is n×100 K, find n.
Physics · Mixed Chapter
JEE Mains

Question

Two blackbody spectral-intensity-versus-wavelength curves A and B have total areas in the ratio 16:1, with A the higher-intensity curve. The temperature for B is 27°C. If the temperature for A is n×100 K, find n.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — Interpret area under spectral intensity curve: Total emitted power per unit area is proportional to the area; Stefan–Boltzmann law gives P/A ∝ T⁴. Step 2 — Area ratio: I₁(total)/I₂(total) = (T₁/T₂)⁴ = 16. Thus T₁/T₂ = 16¹⁄⁴ = 2. Step 3 — Convert temperature B to Kelvin: T₂ = 27+273 = 300 K. Step 4 — Temperature A: T₁ = 2×300=600 K = 6×100 K. Answer: 6.