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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Thermal Properties of Matter

NTA Abhyas 2020 · Physics · Thermal Properties of Matter

Three very large plates of the same area are kept parallel and...

Three very large plates of the 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 2T2T and 3T3T respectively. The temperature of the middle plate under steady state condition is&Three very large plates of the same area are kept parallel and close to each other. They are considered as ideal black

Options

  1. A(652)1/4T\left(\dfrac{65}{2}\right)1 / 4\text{T}
  2. B(974)1/4T\left(\dfrac{97}{4}\right)1 / 4\text{T}
  3. C(972)1/4T\left(\dfrac{97}{2}\right)1 / 4\text{T}
  4. D(97)1/4T\left(97\right)1 / 4\text{T}

Correct answer

C. (972)1/4T\left(\dfrac{97}{2}\right)1 / 4\text{T}

Step-by-step solution

σA(2T)4+σA(3T)4=σ2A(T′)4\sigma \text{A} {\left(2 \text{T}\right)}^{4} + \sigma \text{A} {\left(3 \text{T}\right)}^{4} = \sigma 2 \text{A} {\left(T^{′}\right)}^{4}

16T4+81T4=2(T′)41 6 T^{4} + 8 1 T^{4} = 2 {\left(T^{′}\right)}^{4}

97T4=2(T′)49 7 T^{4} = 2 {\left(T^{′}\right)}^{4}

(T′)4=972T4{\left(T^{′}\right)}^{4} = \dfrac{9 7}{2} T^{4}

∴T′=(972)1/4T∴ T^{′} = ( \dfrac{9 7}{2} {)}^{1 / 4} \text{T}

Three very large plates of the same area are kept parallel and close to each other. They are considered as ideal black
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