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Chapter 37: Q7- (page 1081)

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

Expert verified

At the wavelength of 2.421μm, ceramic cube has its emission spectrum peak.

Step by step solution

01

Step-1 Given information

We have given that cube has a side l=3.0cmand radiates heat P=630Wand e=1and

We have to find out the wavelength.

02

Step 2- Formula used

Using Stefan's Law,

which states that P=eσAT4

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

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

A=6×3×3cm2

A=54cm2

03

Step 3-Simplify

Using Wien's law,

which states thatλ(nm)=2.9×106(nm.K)Tlet this be equation 1

and T=(PσeA)14

Putting the value of T in equation 1,

λ(nm)=2.9×106(PσeA)14

On solving We get

λ=2421nm

Changing units,

we get,

λ=2.421μm

The wavelength of ceramic cube is2.421μm

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