A black plane surface at a constant high temperature $T_{1}$ is parallel to another black plane surface at a constant lower temperature $T_{2}$ . Between the plates is vacuum. In order to reduce the heat flow due to radiation, a heat shield consisting of two thin black plates, thermally isolated from each other is placed between the warm and the cold surfaces and parallel to these. After sometime stationary conditions are obtained.
By what factor f is the stationary heat flow reduced due to the presence of the heat shield? Neglect the effects due to finite size of the surfaces.

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answer is B.

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Detailed Solution

Under steady state conditions the net rate of the heat flow per unit area is the same everywhere.
$H = σ (T_{1}^{4} - T_{3}^{4})$
$H = σ (T_{3}^{4} - T_{4}^{4})$
$H = σ (T_{4}^{4} - T_{2}^{4})$
Adding these three equations, we get
$3 H = σ (T_{1}^{4} - T_{2}^{4}) = H_{0}$
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Here $H_{0} = σ (T_{1}^{4} - T_{2}^{4})$ is the rate of heat flow per unit area in the absence of the shields.
$∴$ The desired fraction $f = \frac{H}{H_{0}} = \frac{1}{3}$