Two rods $$1$$ and $$2$$ have cross sectional areas A and $$2A$$. Ratio of their length is $$1$$ : $$2$$, ratio of their coefficient of thermal conductivities is $$4$$ : x. When the ends of the rods are maintained at temperatures θ$$1oC$$ and θ$$2oC$$ $$($$θ$$1$$θ$$2)$$, they conduct heat at the same rate. Then the value of x is

Question

Two rods $$1$$ and $$2$$ have cross sectional areas A and $$2A$$. Ratio of their length is $$1$$ : $$2$$, ratio of their coefficient of thermal conductivities is $$4$$ : x. When the ends of the rods are maintained at temperatures θ$$1oC$$ and θ$$2oC$$ $$($$θ$$1$$>θ$$2)$$, they conduct heat at the same rate. Then the value of x is

Infinity Learn · Accepted Answer

In steady state $$K1A($$θ$$1$$−θ$$2)l1=K22A($$θ$$1$$−θ$$2)l2$$⇒$$K1K2=l1l2.2$$⇒$$4x=12.2$$⇒$$x=4$$

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Two rods 1 and 2 have cross sectional areas A and 2A. Ratio of their length is 1 : 2, ratio of their coefficient of thermal conductivities is 4 : x. When the ends of the rods are maintained at temperatures θ1oC and θ2oC (θ1>θ2), they conduct heat at the same rate. Then the value of x is

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