A) \[{{\left( \frac{65}{2} \right)}^{1/4}}T\]
B) \[{{\left( \frac{97}{4} \right)}^{1/4}}T\]
C) \[{{\left( \frac{97}{2} \right)}^{1/4}}T\]
D) \[{{(97)}^{1/4}}T\]
Correct Answer: C
Solution :
[c] : Let T' be the temperature of i n m the middle plate (II) and A be area of each plate. Under steady state, the rate of energy received by the middle plate is equal to 2T r 3T rate of energy emitted by it. i.e.,\[\sigma A{{(3T)}^{4}}-\sigma A{{(T')}^{4}}=\sigma A{{(T')}^{4}}-\sigma A{{(2T)}^{4}}\] or\[\sigma A[{{(3T)}^{4}}-{{(T')}^{4}}]=\sigma A[{{(T')}^{4}}-{{(2T)}^{4}}]\] or\[[{{(3T)}^{4}}-{{(T')}^{4}}={{(T')}^{4}}-{{(2T)}^{4}}\] or\[2{{(T')}^{4}}={{T}^{4}}({{3}^{4}}+{{2}^{4}})={{T}^{4}}(81+16)=97{{T}^{4}}\] or\[T{{'}^{4}}=\frac{97}{2}{{T}^{4}}orT'={{\left( \frac{97}{2} \right)}^{1/4}}T\]You need to login to perform this action.
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