Question

Two bodies a and b have emissivities 0.5 and 0.8 respectively. At some temperatures the two bodies have maximum spectral emissive powers at wavelength 8000 a and 4000 a respectively. The ratio of their emissive powers at these temperatures is?

Answer 1

Answer:

The ratio of the temperatures is 1:2.

Explanation:

Given that,

Emissivity of a = 0.5

Emissivity of b = 0.8

Wavelength of a =8000

Wave length of b = 4000

Let the body have temperature T₁ and T₂ respectively

Using Wien's displacement law

$\lambda T=constant$

For body a and b

We need to calculate the ratio of their emissive powers at these temperatures

$\lambda_{a}T_{a}=\lambda_{b}T_{b}$

Put the value into the formula

$8000\times T_{a}=4000\times T_{b}$

$\dfrac{T_{a}}{T_{b}}=\dfrac{4000}{8000}$

$\dfrac{T_{a}}{T_{b}}=\dfrac{1}{2}$

Hence,  The ratio of the temperatures is 1:2.