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Question

A wall is made up of two layers A and B. The thickness of the two layers is the same, but materials are different. The thermal conductivity of A is double than that of B. In thermal equilibrium the temperature difference between the two ends is 3 6 to the power of o end exponent C. Then the difference of temperature at the two surfaces of A will be

  1. 6 to the power of o end exponent C    
  2. 1 2 to the power of o end exponent C    
  3. 1 8 to the power of o end exponent C    
  4. 2 4 to the power of o end exponent C    

The correct answer is: 1 2 to the power of o end exponent C


    Suppose thickness of each wall is x then open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript c o m b i n a t i o n end subscript equals open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript A end subscriptÞ fraction numerator K subscript S end subscript A left parenthesis theta subscript 1 end subscript minus theta subscript 2 end subscript right parenthesis over denominator 2 x end fraction equals fraction numerator 2 K A left parenthesis theta subscript 1 end subscript minus theta right parenthesis over denominator x end fraction
    because K subscript S end subscript equals fraction numerator 2 cross times 2 K cross times K over denominator left parenthesis 2 K plus K right parenthesis end fraction equals fraction numerator 4 over denominator 3 end fraction K and left parenthesis theta subscript 1 end subscript minus theta subscript 2 end subscript right parenthesis equals 36 degree
    Þ fraction numerator fraction numerator 4 over denominator 3 end fraction K A cross times 36 over denominator 2 x end fraction equals fraction numerator 2 K A left parenthesis theta subscript 1 end subscript minus theta right parenthesis over denominator x end fraction
    Hence temperature difference across wall A is
    left parenthesis theta subscript 1 end subscript minus theta right parenthesis equals 1 2 to the power of o end exponent C

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