Questions

A slab consists of two layers of two different materials of same thickness having thermal conductivities ${\text{K}}_{1}$ and ${\text{K}}_{2}$, the equivalent conductivity of the combination in series is

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a
K1+K2
b
K1+K22
c
2K1K2K1+K2
d
K1+K22K1K2
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detailed solution

Correct option is C

In series slabs are,for 2 slabs of same thickness l having coefficient of thermal conductivities K1,K2 is since, in series effective resistance is Rseries=R1+R2 Resistance is R=lKA, here l = thickness, K=coefficient of thermal conductivity, A=area of cross section Rseries=R1+R2 l+lKseriesA=lK1A+lK2A  ⇒Kseries=2K1K2K1+K2

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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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