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

Expert verified

The wavelenght will beλ=2.421μm

Step by step solution

01

Given Information

We have been given that:

Side of cube = 3.0cm

Power =630W

02

Calculation

On applying Stefen's Law:

P=eσAT4

HerePstands for emmisive power,estands for emissivity,σis Stefen's constant,Ais area andTis temperature in Kelvin.

We get the expression for T : localid="1650119591603" role="math" T=PeσA14 - ( i )

Total surface of the cube: localid="1650119604767" Anet=6×3×3=54cm2

On Applying Wien's law:

localid="1649748840661" λ(nm)=2.9×106(nm·K)T

localid="1650119631751" λ(nm)=2.9×106(nm·K)PeσA14 - using ( i )

localid="1650119670148" λ(nm)=2.9×106(nm·K)6301×5.67×10-8×54×10-414

localid="1649748874919" λ=2421nm=2.421μm

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