Three concentric thin spherical shells are shown in figure. Outer most sphere can't radiate in outer space. The inner most and the outer most shells are maintained at T 1 K & T 2 K respective

Question

Three concentric thin spherical shells are shown in figure. Outer most sphere can't radiate in outer space. The inner most and the outer most shells are maintained at $T_{1} K$ & $T_{2} K$ respectively. Assume the three shells behaves as black body. The steady state temperature of the middle shell is $(\frac{T _{1}^{4}}{x} + \frac{T _{2}^{4}}{y})^{1/4}$ . Value of $x + y$ is

TestHub · Accepted Answer

In steady state, the net heat transfer rate to the middle shell is zero: it absorbs radiation from the inner shell and emits to the outer shell.

$q^{4} = \frac{T _{1}^{4}}{5} + \frac{T _{2}^{4}}{( 5/4 )}$

Comparing with $(\frac{T _{1}^{4}}{x} + \frac{T _{2}^{4}}{y})^{1/4}$ : x = 5 and y = 5/4 = 1.25.

$x + y = 5 + 1.25 = 6.25$

Answer: 6.25

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