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# A wall has two layers A and B, each made of different material, “A” has thickness 10 cm, while “B” has thickness 20cm, their coefficients of conductivities are in the ratio of 3:1, a constant temperature difference of  ${35}^{\circ }\text{c}$ exists across the wall, the difference of temperature across the layer “A” is

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a
28∘c
b
14∘c
c
5∘c
d
3.5∘c
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detailed solution

Correct option is C

rate of transfer of heat is Qt=KA(θ1-θ2)l here k is coefficient of thermal conductivity A is area of cross section θ1-θ2 is temperature difference l is length of width  at steady state , heat transfer is constant temperature across layer  A is θ1-θ  temperature across layer  B is θ-θ2  Qt=K1A(θ1-θ)l1=K2A(θ-θ2)l2 3(θ1-θ)=12(θ-θ2)---(1) (θ1-θ2)=350C⇒θ2=θ1-35---(2) on substituting the value of θ2 from eqn(2) in eqn(1) ⇒3θ1-3θ=12θ-12θ1-35⇒6θ1-6θ=θ-θ1+35⇒7θ1-θ=35 θ1-θ=50C=temperature difference across layer A

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Two rods of length ${\mathrm{d}}_{1}$ and ${\mathrm{d}}_{2}$ and coefficients of thermal conductivities ${\mathrm{K}}_{1}$ and ${\mathrm{K}}_{2}$ are kept touching each other. Both have the same area of cross-section. The equivalent of thermal conductivity is

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