Three very large plates of same area are kept parallel and close … - Vidyadip

MCQ

Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures $2T$ and $3T$ respectively. The temperature of the middle (i.e. second) plate under steady state condition is

A
$\left (\frac{65}{2} \right )^{1/4} T$
B
$\left (\frac{97}{4} \right )^{1/4} T$
✓
$\left (\frac{97}{2} \right )^{1/4} T$
D
$(97)^{1/4}T$

✓

Answer

Correct option: C.

$\left (\frac{97}{2} \right )^{1/4} T$

c
For steady state, $P_{\text {net received }}=P_{\text {rem emitted }}$

$\sigma A\left(\theta^{4}-(2 T)^{4}\right)=\sigma A\left[(3 T)^{4}-\theta^{4}\right]$

$\Rightarrow \theta^{4}-16 T^{4}=81 T^{4}-\theta^{4} \Rightarrow \theta=\left(\frac{97}{2}\right)^{1 / 4} T$

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