The two ends of a metal rod are maintained at temperatures $$100$$°C and $$110$$° C. The rate of heat flow in the rod is found to be $$4.0$$ $$J/s$$. If the ends are maintained at temperatures $$200$$°C and $$210$$°C, the rate of heat flow will be

Question

The two ends of a metal rod are maintained at temperatures $$100$$°C  and $$110$$° C. The rate of heat flow in the rod is found to be $$4.0$$ $$J/s$$. If the ends are maintained at temperatures $$200$$°C and $$210$$°C, the rate of heat flow will be

Infinity Learn · Accepted Answer

Rate of heat flow through a rod is given by $$dQdt=-KAdTdx$$ Let length of the rod be L .  Case I : $$dTdx=$$ΔTΔ$$x=110-100L=10L$$∴  $$dQ1dt=-KA10L$$                                            . . . .(i) Also, $$dQ1dt=4$$ J $$s-1$$                                           . . . .(ii) Case II : $$dTdx=$$ΔTΔ$$x=210-200L=10L$$∴  $$dQ2dt=-KA10L$$                                               . . . .(iii) So, from equations (i), (ii) and (iii) $$dQ2dt=dQ1dt=4$$ J $$s-1$$

The two ends of a metal rod are maintained at temperatures 100°C and 110° C. The rate of heat flow in the rod is found to be 4.0 J/s. If the ends are maintained at temperatures 200°C and 210°C, the rate of heat flow will be

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