Question 323: Properties of Matter

Question

The power radiated by a black body is P and it
radiates maximum energy at wavelength, $$\lambda $$0
. If
the temperature of the black body is now
changed so that it radiates maximum energy at
wavelength $${3 \over 4}{\lambda _0}$$, the power radiated by it
becomes nP. The value of n is

Accepted Answer

From Wien's law, $$\lambda $$
max
T = constant
$$ 	herefore $$ $$\lambda $$
max
1
T
1
= $$\lambda $$
max
2
T
2
$$ \Rightarrow $$ $$\lambda $$
0
T
1
= $${{3{\lambda _0}} \over 4}$$T
2
$$ \Rightarrow $$ $${{T_2} \over T_1} = {4 \over 3}$$
According to Stefan-Boltzmann law, energy emitted
unit time by a black body is Ae$$\sigma $$T
4
,
$$ 	herefore $$ P $$ \propto $$ T
4
So $${{{P_2}} \over {{P_1}}} = {\left( {{{{T_2}} \over {{T_1}}}} ight)^4}$$ = $${\left( {{4 \over 3}} ight)^4}$$
Here, P
2
= nP and P
1
= P
So, $${{nP} \over P} = n = {\left( {{{{T_2}} \over {{T_1}}}} ight)^4} = {\left( {{4 \over 3}} ight)^4} = {{256} \over {81}}$$

Answer

$${3 \over 4}$$

Answer

$${4 \over 3}$$

Answer

$${{256} \over {81}}$$

Answer

$${{81} \over {256}}$$

Properties of Matter

The power radiated by a black body is P and it radiates maximum energy at wavelength, $\lambda 0 . If the temperature of the black body is now changed so that it radiates maximum energy at wavelength {3 \over 4}{\lambda _0}$, the power radiated by it becomes nP. The value of n is

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