Question

The surface temperature of the sun is ' $T$ K and the solar constant for a plate is ' $s$ '. The sun subtends an angle $\theta$ at the planet. Then:(a) $s \propto T^{i}$ (b) $s \propto T^{2}$ (c) $s \propto \theta^{2}$ (d) $s \propto \theta$

Name: Problem 44, Chapter 18: Arihant AIEEE Physics
Uploaded: 2021-09-24T19:15:54-08:00
Duration: 3 min 30 s
Channel: Saman Zulfiqar
Description: The surface temperature of the sun is ' T K and the solar constant for a plate is ' s '. The sun subtends an angle θat the planet. Then:(a) s ∝T^i (b) s ∝T^2 (c) s ∝θ^2 (d) s ∝θ

   The surface temperature of the sun is ' $T$ K and the solar constant for a plate is ' $s$ '. The sun subtends an angle $\theta$ at the planet. Then:(a) $s \propto T^{i}$
(b) $s \propto T^{2}$
(c) $s \propto \theta^{2}$
(d) $s \propto \theta$

Arihant AIEEE Physics

D.B. Singh 2006 Edition

Chapter 18, Problem 44

Instant Answer

Solved by Expert Saman Zulfiqar

09/24/2021

Step 1

Mathematically, it is represented as: \[ P = \sigma A T^{4} \] where: $P$ is the total power radiated, $\sigma$ is the Stefan-Boltzmann constant, $A$ is the surface area of the sun, and $T$ is the surface temperature of the sun. Show more…

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The surface temperature of the sun is ' $T$ K and the solar constant for a plate is ' $s$ '. The sun subtends an angle $\theta$ at the planet. Then:(a) $s \propto T^{i}$ (b) $s \propto T^{2}$ (c) $s \propto \theta^{2}$ (d) $s \propto \theta$

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Key Concepts

Stefan?Boltzmann Law

This law states that the power emitted per unit area by a black body is proportional to the fourth power of its temperature (P ? T^4). In astrophysics, it is used to compute the luminosity of stars, relating the surface temperature to the total energy output, which is key to determining the radiative flux received at a distance.

Angular Size and Solid Angle

In radiative transfer, when a source appears under a small angle, the fraction of its luminosity intercepted by a surface depends on the solid angle it subtends. For small angular extents, the solid angle scales as the square of the subtended angle (?^2). This relationship is crucial when linking the apparent size of an astronomical object to the flux received.

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