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10.2 , transmission of heat — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics10.2 , transmission of heat1 Mark
MCQ
The spectral emissive power $E_\lambda $ for a body at temperature $T_1$ is plotted against the wavelength and area under the curve is found to be $A$. At a different temperature $T_2$ the area is found to be $9A$. Then $\lambda _1/\lambda _2 =$
  • A
    $3$
  • B
    $1/3$
  • C
    $1/\sqrt 3 $
  • ✓
    $\sqrt 3 $
✓

Answer

Correct option: D.
$\sqrt 3 $
d
The spectral emissive power is directly proportional to the fourth power of the absolute temperature.

$E_{\lambda}=k T^{4}$

$E_{1}=k T_{1}^{4}=A$

$E_{2}=k T_{2}^{4}=9 A$

$\frac{E_{2}}{E_{1}}=\left(\frac{T_{2}}{T_{1}}\right)^{4}=9$

$\frac{T_{2}}{T_{1}}=\sqrt{3}$

$T_{2}=\sqrt{3} T_{1}$

According to Wien's displacement law.

$\lambda T=b=$ constant

$\lambda_{1} T_{1}=\lambda_{2} T_{2}$

$\frac{\lambda_{1}}{\lambda_{2}}=\frac{T_{2}}{T_{1}}=\sqrt{3}$

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