Chapter 37: Q7- (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

At the wavelength of $2.421 μ m$ , ceramic cube has its emission spectrum peak.

Step by step solution

Step-1 Given information

We have given that cube has a side $l = 3.0 c m$ and radiates heat $P = 630 W$ and $e = 1$ and

We have to find out the wavelength.

Step 2- Formula used

Using Stefan's Law,

which states that $P = e σ A T^{4}$

where P is heat radiated ,A is the area, T is the temperature and $σ$ is Stefan-Boltzmann constant

Find net A (net area of surface of the cube)

$A = 6 \times 3 \times 3 c m^{2}$

$A = 54 c m^{2}$

Step 3-Simplify

Using Wien's law,

which states that $λ (n m) = \frac{2.9 \times 10^{6} (n m . K)}{T}$ let this be equation 1

and $T = {(\frac{P}{σ e A})}^{\frac{1}{4}}$

Putting the value of T in equation 1,

$λ (n m) = \frac{2.9 \times 10^{6}}{{(\frac{P}{σ e A})}^{\frac{1}{4}}}$

On solving We get

$λ = 2421 n m$

Changing units,

we get,

$λ = 2.421 μ m$

The wavelength of ceramic cube is $2.421 μ m$

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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

Step-1 Given information

Step 2- Formula used

Step 3-Simplify

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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? Assumee=1

Short Answer

Step by step solution

Step-1 Given information

Step 2- Formula used

Step 3-Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Rotational Dynamics

Medical Physics

Electricity

Translational Dynamics

Physics of Motion

Space 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 $e = 1$