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 $$35$$∘c exists across the wall, the difference of temperature across the layer “A” is

Question

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  $$35$$∘c exists across the wall, the difference of temperature across the layer “A” is

Infinity Learn · Accepted Answer

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

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