Chapter 37: Q. 7 (page 1081)

A ceramic cube $3.0 c m$ on each side radiates heat at $630 W$ . At what wavelength, in $μ m$ , does its emission spectrum peak? Assume $e = 1$ .

Short Answer

Expert verified

The wavelenght will be $λ = 2.421 μ m$

Step by step solution

Given Information

We have been given that:

Side of cube = $3.0 c m$

Power = $630 W$

Calculation

On applying Stefen's Law:

$P = e σ A T^{4}$

Here $P$ stands for emmisive power, $e$ stands for emissivity, $σ$ is Stefen's constant, $A$ is area and $T$ is temperature in Kelvin.

We get the expression for T : localid="1650119591603" role="math" $T = {(\frac{P}{e σ A})}^{\frac{1}{4}}$ - ( i )

Total surface of the cube: localid="1650119604767" $A_{n e t} = 6 \times 3 \times 3 = 54 c m^{2}$

On Applying Wien's law:

localid="1649748840661" $λ (n m) = \frac{2.9 \times 10^{6} (n m \cdot K)}{T}$

localid="1650119631751" $λ (n m) = \frac{2.9 \times 10^{6} (n m \cdot K)}{{(\frac{P}{e σ A})}^{\frac{1}{4}}}$ - using ( i )

localid="1650119670148" $λ (n m) = \frac{2.9 \times 10^{6} (n m \cdot K)}{{(\frac{630}{1 \times 5.67 \times 10^{- 8} \times 54 \times 10^{- 4}})}^{\frac{1}{4}}}$

localid="1649748874919" $λ = 2421 n m = 2.421 μ m$

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A ceramic cube $3.0 c m$ on each side radiates heat at $630 W$ . At what wavelength, in $μ m$ , does its emission spectrum peak? Assume $e = 1$ .

Short Answer

Step by step solution

Given Information

Calculation

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A ceramic cube 3.0cmon each side radiates heat at 630W. At what wavelength, in μm, does its emission spectrum peak? Assume e=1.

Short Answer

Step by step solution

Given Information

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Atoms and Radioactivity

Magnetism and Electromagnetic Induction

Mechanics and Materials

Nuclear Physics

Wave Optics

Fields in Physics

Study anywhere. Anytime. Across all devices.

A ceramic cube $3.0 c m$ on each side radiates heat at $630 W$ . At what wavelength, in $μ m$ , does its emission spectrum peak? Assume $e = 1$ .