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Three highly conducting concentric spherical shells (acting as black body) of radii $r_{1}, r_{2}$ and $r_{3}$ are kept in vacuum. The region between the shells is evacuated and they can exchange energy only by radiation. Inside the inner most shell there is a heater of constant power P. In steady state, ( $σ$ = Stefan’s constant)

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Temperature of innermost shell is ${(\frac{P}{4 π σ})}^{1 / 4} {(\frac{1}{r_{1}^{2}} - \frac{1}{r_{2}^{2}})}^{1 / 4}$

Temperature of outermost shell is ${(\frac{P}{4 π σ r_{3}^{2}})}^{1 / 4}$

If both outer and middle shell were removed, the temperature of innermost shell would decrease

Temperature of middle shell is ${(\frac{P}{4 π σ})}^{1 / 4} {(\frac{1}{r_{3}^{2}} + \frac{1}{r_{2}^{2}})}^{1 / 4}$

answer is A, B, D.

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Detailed Solution

Power leaving the system = P
$P = σ (4 π C^{2}) T_{C}^{4}$
Net power leaving B = P
$P = σ (4 π b^{2}) T_{B}^{4} - σ (4 π b^{2}) T_{C}^{4}$

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