Question

A black body has a temperature of 2900k when it cools wave length corresponding to maximum energy density changes by 9 micron then the temperature to which the body is cooled would be

Answer 1

Lambda = b/T by weins eqn

Answer 2

Answer:

The temperature to which the body is cooled would be 279.5K.

Explanation:

From the Wein's displacement law we have,

$\lambda T=b$         (1)

Where,

λ=wavelength of the light corresponding to temperature T

T=temperature

b=wein displacement constant=2.8×10⁻³K-m

From the question we have,

Δλ=9μm=9×10⁻⁶m

T₁=2900K

By substituting the value of T₁ in equation (1) we get;

$\lambda_1\times 2900=2.8\times 10^-^3$

$\lambda_1=\frac{2.8}{29} \times 10^-^5$

$\lambda_1=0.96\times 10^-^6m$       (2)

And,

$\lambda_2-\lambda_1=9\times 10^-^6$

$\lambda_2=9\times 10^-^6+0.96\times 10^-^6$

$\lambda_2=9.96\times 10^-^6m$         (3)

By using equation (1) we get;

$\lambda_1 T_1=\lambda_2 T_2$        (4)

By substituting the required values in equation (4) we get;

$0.96\times 10^-^6\times 2900=9.96\times 10^-^6\times T_2$

$T_2=\frac{0.96\times 10^-^6\times 2900}{9.96\times 10^-^6}$

$T_2=279.5K$

Hence, the temperature to which the body is cooled would be 279.5K.