Three discs x, y and z having radii 2 m, 3 m and 6 m respectively are coated on outer surfaces. The wavelength corresponding to maximum intensity are 300 nm, 400 nm and 500 nm respectively. If Px, Py and Pz are power radiated by them respectively then (a) Px is maximum (b) Pz is maximum (c) Py is maximum (d) Px = Py = Pz

Answer: (b). P = σ A T⁴ with A ∝ r² and T ∝ (1)/(λm), so P ∝ (r²)/(λm⁴). Px ∝ (2²)/(3⁴) = 4/81 ≈ 0.049 Py ∝ (3²)/(4⁴) = 9/256 ≈ 0.035, Pz ∝ (6²)/(5⁴) = 36/625 ≈ 0.058 So the answer is (b) Pz is maximum.

Three discs x, y and z having radii 2 m, 3 m and 6 m respectively are… | MHT CET 2022 (11 Aug, Shift 2)

Q85MHT CET 2022 · 11 AUG · SHIFT 2Difficult

Thermal Radiation: Black Body, Stefan & Wien

Three discs $x, y$ and $z$ having radii $2\text{ m}, 3\text{ m}$ and $6\text{ m}$ respectively are coated on outer surfaces. The wavelength corresponding to maximum intensity are $300\text{ nm}, 400\text{ nm}$ and $500\text{ nm}$ respectively. If $P_x, P_y$ and $P_z$ are power radiated by them respectively then

Show answer and solution

Answer: (b)

$P = \sigma A T^4$ with $A \propto r^2$ and $T \propto \frac{1}{\lambda_m}$ , so $P \propto \frac{r^2}{\lambda_m^4}$ .
$P_x \propto \frac{2^2}{3^4} = \frac{4}{81} \approx 0.049$
$P_y \propto \frac{3^2}{4^4} = \frac{9}{256} \approx 0.035$ , $P_z \propto \frac{6^2}{5^4} = \frac{36}{625} \approx 0.058$
So the answer is (b) $P_z$ is maximum.

Report a mistake

Thermal Radiation: Black Body, Stefan & Wien question from MHT CET 2022 (11 Aug, Shift 2)

More questions on Thermal Radiation: Black Body, Stefan & Wien