You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XIII

Physics

Stefan-Boltzman's Law

Two spherical...

Question

Two spherical black bodies $A$ and $B$ , having radii $r_{A}$ and $r_{B},$ where $r_{B} = 2 r_{A}$ emit radiation with peak intensities at wavelength $400 nm$ and $800 nm$ respectively. If their temperatures are $T_{A}$ and $T_{B}$ respectively in Kelvin scale, their emissive powers are $E_{A}$ and $E_{B}$ and energies emitted per second are $P_{A}$ and $P_{B}$ respectively, then

\frac{T_{A}}{T_{B}} = 2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{P_{A}}{P_{B}} = 4

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{E_{A}}{E_{B}} = 8

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{E_{A}}{E_{B}} = 16

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $\frac{E_{A}}{E_{B}} = 16$
Given
$r_{B} = 2 r_{A}$

By Wein’s displacement law, wavelength corresponding to maximum intensity is
$λ_{A} \propto \frac{1}{T}$
$\frac{(λ_{m})_{A}}{(λ_{m})_{B}} = \frac{T_{B}}{T_{A}} = \frac{400}{800}$
$∴ \frac{T_{A}}{T_{B}} = 2$
By Stefan’s law,
$E = σ e T^{4}$
$\frac{E_{A}}{E_{B}} = \frac{T_{A}^{4}}{T_{B}^{4}} = 16$
$\frac{P_{A}}{P_{B}} = \frac{A_{A} T_{A}^{4}}{A_{B} T_{B}^{4}}$
$\frac{P_{A}}{P_{B}} = \frac{4 π r_{A}^{2} T_{A}^{4}}{4 π r_{B}^{2} T_{B}^{4}} = 4$

Suggest Corrections

Similar questions

Q. Two spherical black bodies

A

and

B

, having radii

r_{A}

and

r_{B},

where

r_{B} = 2 r_{A}

emit radiation with peak intensities at wavelength

400 nm

and

800 nm

respectively. If their temperatures are

T_{A}

and

T_{B}

respectively in Kelvin scale, their emissive powers are

E_{A}

and

E_{B}

and energies emitted per second are

P_{A}

and

P_{B}

respectively, then

Q. Two bottles A and B have radii

R_{A}

and

R_{B}

and heights

h_{A}

and

h_{B}

respectively with

R_{B} = 2 R_{A}

and

h_{B} = 2 h_{A}

. These are filled with hot water at

60^{o}

C. Consider that heat loss for the bottles takes place only from side surfaces. If the time the water takes to cool down to

50^{o}

C is

t_{A}

and

t_{B}

for bottles A and B, respectively, then

t_{A}

and

t_{B}

are best related as.

Three bodies $A, B a n d C$ have equal surface area and thermal emissivities in the ratio $e_{A} : e_{B} : e_{C} = 1 : \frac{1}{2} : \frac{1}{4}$ . All the three bodies are radiating at same rate. Their wavelengths corresponding to maximum intensity are $λ_{A}, λ_{B} a n d λ_{C}$ respectively and their temperatures are $T_{A}, T_{B} a n d T_{C}$ on kelvin scale, then select the incorrect statement :