Question

The temperature of the sun is $5500K$and it emits maximum intensity radiation in the yellow region $\left( {5.5 \times {{10}^{ - 7}}m} \right)$. The maximum radiation from the furnace occurs at wavelength $11 \times {10^{ - 7}}m$. The temperature of the furnace is
A. $1125K$
B. $2750K$
C. $5500K$
D. $11000K$

Answer 1

Hint:In this question, we are given the maximum intensity wavelength of the sun and its temperature. We have found the temperature of the furnace whose wavelength is given. So, for such questions we can use the Wien displacement law. Whose expression is ${\lambda _m}T = const$ where ${\lambda _m}$ is the wavelength and $T$ is the temperature.

Complete step by step answer:
According to the Wein displacement law, it states that the black body radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature.
${\lambda _m} \propto \dfrac{1}{T}$ where ${\lambda _m}$ is the maximum wavelength and $T$ is the temperature of the radiation.
Or ${\lambda _m}T = b(const)$
According to the question:
Temperature of the sun is ${T_1}$$ = 5500K$and wavelength be given by ${\lambda _1} = 5.5 \times {10^{ - 7}}m$
And the wavelength of the furnace can be given by ${\lambda _2} = 11 \times {10^{ - 7}}$ and temperature of the furnace=?
Using the Wien displacement law,
${\lambda _1}{T_1} = {\lambda _2}{T_2}$
Putting the values
$5.5 \times {10^{ - 7}} \times 5500 = 11 \times {10^{ - 7}} \times {T_2}$
$\therefore{T_2} = 2750K$
So, Temperature of the furnace is $2750K$

Hence, the correct option is B.

Note:Wien’s Law, named after the German Physicist Wilhelm Wien, tells us that objects of different temperatures emit spectra that peak at different wavelengths. Hotter objects emit radiations of shorter wavelength and hence they appear blue. Similarly, cooler objects emit radiations of longer wavelength and hence they appear reddish.Wien displacement law has nothing as displacement as its name. The term maximum wavelength is used for the wavelength with maximum energy. The value of constant for Wien displacement law is $b = 2.89 \times {10^{ - 3}}mK$