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Chapter 28: Problem 2822

What is the units of emissive power in stefan's law? (A) \(\mathrm{Ws}^{-1}\) (B) W (C) \(\mathrm{Ws}^{-1} \mathrm{~m}^{-2}\) (D) \(\mathrm{Wm}^{-2}\)

Short Answer

Expert verified
The correct units of emissive power in Stefan's Law are (D) \(\mathrm{Wm}^{-2}\).

Step by step solution

01

Understand Stefan's Law

Stefan's law is given by: \[E = \sigma T^4\] where E is the emissive power (the power radiated per unit surface area), T is the temperature in kelvins, and σ is the Stefan-Boltzmann constant, which equals \(5.67 \times 10^{-8} \mathrm{Wm}^{-2}\mathrm{K}^{-4}\).
02

Check units for each given option

Consider the units in the formula: emissive power (E) equals the product of the Stefan-Boltzmann constant (σ) and temperature to the fourth power (T^4). (A) \(\mathrm{Ws}^{-1}\): This indicates work done per second, which doesn't account for surface area. (B) W: Watts, a unit of power, but it doesn't account for surface area. (C) \(\mathrm{Ws}^{-1} \mathrm{~m}^{-2}\): This indicates work done per second per square meter which isn't right. (D) \(\mathrm{Wm}^{-2}\): This indicates power per unit surface area, which is consistent with the description of emissive power.
03

Choose the correct units

Based on the analysis in step 2, option (D) \(\mathrm{Wm}^{-2}\) represents the correct units of emissive power in Stefan's Law.

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Most popular questions from this chapter

Two spheres of the same material have radii \(1 \mathrm{~m}\) and $4 \mathrm{~m}\( and temperatures \)2000 \mathrm{k}\( and \)4000 \mathrm{k}$ respectively. If the energy radiated by the spheres are \(E_{1}\) and \(E_{2}\) respectively then find ratio of \(\left(\mathrm{E}_{1} / \mathrm{E}_{2}\right)\) (A) \(1: 256\) (B) \(256: 1\) (C) \(16: 1\) (D) \(1: 16\)

A sphere, a cube and a thin circular plate are all made of the same material, have the same mass and are initially heated to a temperature of $200^{\circ} \mathrm{C}$. Arrange then in the ascending order of rate of cooling. (A) sphere, plate, cube (B) sphere, cube, plate (C) cube, sphere, plate (D) plate, cube, sphere

A liquid takes 5 minute to cool from \(80^{\circ} \mathrm{C}\) to $50^{\circ} \mathrm{C}\(. The temperature of the surrounding is \)20^{\circ} \mathrm{C}$. What is the time it will take to \(\operatorname{cool}\) from $60^{\circ} \mathrm{C}\( to \)30^{\circ} \mathrm{C}$ ? (A) \(9 \mathrm{~min}\) (B) \(5 \mathrm{~min}\) (C) \(12 \mathrm{~min}\) (D) \(6 \mathrm{~min}\)

A body cools in 5 minute from \(60^{\circ} \mathrm{C}\) to $40^{\circ} \mathrm{C}\(. The temperature of the surroundings is \)10^{\circ} \mathrm{C}$. What is its temperature after the next 5 minute? (A) \(32^{\circ} \mathrm{C}\) (B) \(24^{\circ} \mathrm{C}\) (C) \(28^{\circ} \mathrm{C}\) (D) \(30^{\circ} \mathrm{C}\)
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