(C) According to Wien's displacement law, $\lambda_m T = \text{constant}$.This implies that $\lambda_m \propto 1/T$. Therefore, as the temperature $T$

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(C) According to Wien's displacement law, $\lambda_m T = \text{constant}$.This implies that $\lambda_m \propto 1/T$. Therefore, as the temperature $T$ increases, the peak emission wavelength $\lambda_m$ decreases. Thus, the Assertion is correct.According to the Stefan-Boltzmann law, the total energy radiated per unit area per unit time is $E = \sigma T^4$. This law relates energy to temperature, not the peak wavelength. The peak wavelength is governed by Wien's displacement law, not the fourth power of temperature. Thus, the Reason is incorrect.

Class 11 Physics 10-2.Heat Transfer Spectral Emissive Power and Wien's Displacement Law

Easy

$Assertion :$ For higher temperature, the peak emission wavelength of a blackbody shifts to lower wavelengths.
$Reason :$ Peak emission wavelength of a blackbody is proportional to the fourth power of temperature.

AIIMS 2005 All AIIMS

A
If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
B
If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
C
If the Assertion is correct but Reason is incorrect.
D
If both the Assertion and Reason are incorrect.

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10-2.Heat Transfer

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Spectral Emissive Power and Wien's Displacement Law

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$Assertion :$ For higher temperature, the peak emission wavelength of a blackbody shifts to lower wavelengths.$Reason :$ Peak emission wavelength of a blackbody is proportional to the fourth power of temperature.

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$A$ black body at a temperature of $1640 \ K$ has the wavelength corresponding to maximum emission equal to $1.75 \ \mu m$. Assuming the moon to be a perfectly black body,the temperature of the moon,if the wavelength corresponding to maximum emission is $14.35 \ \mu m$,is ...... $K$.

Ordinary bodies $P$ and $Q$ radiate maximum energy with a wavelength difference of $3 \mu m$. The absolute temperature of body $P$ is four times that of $Q$. The wavelength at which body $Q$ radiates maximum energy is (in $\mu m$)

$A$ black body emits radiations of maximum intensity at a wavelength of $5000 \mathring A$,when the temperature of the body is $1227^{\circ}C$. If the temperature of the body is increased by $1000^{\circ}C$,the maximum intensity of emitted radiation would be observed at..... $\mathring A$.

Four pieces of iron heated in a furnace to different temperatures show different colours listed below. Which one has the highest temperature?

The wavelength of maximum energy released during an atomic explosion was $2.93 \times 10^{-10} \, m$. The maximum temperature attained must be (Wien's constant $b = 2.93 \times 10^{-3} \, mK$).

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$Assertion :$ For higher temperature, the peak emission wavelength of a blackbody shifts to lower wavelengths.
$Reason :$ Peak emission wavelength of a blackbody is proportional to the fourth power of temperature.