Chapter 37: Q. 5 (page 1081)

A $2.0 - c m -$ diameter metal sphere is glowing red, but a spectrum shows that its emission spectrum peaks at an infrared wavelength of $2.0 m m$ .How much power does the sphere radiate? Assume $e = 1 .$

Short Answer

Expert verified

The power that sphere radiates is $3.1 \times 10^{- 10} W a t t$

Step by step solution

Given Information

We are given that diameter of metal sphere is $2.0 - c m$ , infrared wavelength of spectrum is $2.0 m m$ and $e = 1$ .

We are asked to find power that the sphere radiates.

Simplify

We are given with the diameter of metal sphere , we will find radius of sphere

$r = \frac{d}{2} = \frac{2 c m}{2} = 1 c m$

We will convert cm into m $\Rightarrow 1 c m = 0.01 m$

According to Wien 's law $\Rightarrow λ = \frac{2.9 \times 10^{6} (n m . k)}{T}$

We can find the value of T from this equation, $T = \frac{2.90 \times 10^{6} (n m . k)}{2 \times 10^{6} n m} = 1.45 K$

now power radiated by sphere is given by ,

Power $= e σ A T^{4}$ $= 1 \times (5.67 \times 10^{- 8}) \times 4 π \times {(0.01)}^{2} \times {(1.45)}^{4}$ $= 3.1 \times 10^{- 10} W a t t$

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A $2.0 - c m -$ diameter metal sphere is glowing red, but a spectrum shows that its emission spectrum peaks at an infrared wavelength of $2.0 m m$ .How much power does the sphere radiate? Assume $e = 1 .$

Short Answer

Step by step solution

Given Information

Simplify

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A2.0-cm-diameter metal sphere is glowing red, but a spectrum shows that its emission spectrum peaks at an infrared wavelength of 2.0mm.How much power does the sphere radiate? Assumee=1.

Short Answer

Step by step solution

Given Information

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Geometrical and Physical Optics

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Study anywhere. Anytime. Across all devices.

A $2.0 - c m -$ diameter metal sphere is glowing red, but a spectrum shows that its emission spectrum peaks at an infrared wavelength of $2.0 m m$ .How much power does the sphere radiate? Assume $e = 1 .$