Two rods are taken having same length and area and of the same material are joined side by side, heat is allowed to flow through them for $$12$$ minutes. If now the rods are joined in parallel, then how much time will it take to flow the same amount of heat?

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Infinity Learn · Accepted Answer

in Series time of flow of heat $$ist1=12$$ minutes  amount of heat that flows in two rods when in series is  $$Q1=KseriesA($$θ$$1-$$θ$$2)2lt1----(1)$$  here Kseries is coefficient of thermal conductivity when rods  are in series  A is area of cross section  θ$$1$$,θ$$2$$ is temperatures at their each end  l is length of rod  $$t1$$ is time of flow of heat     In series, effective coefficeint of thermal conductivity is Kseries,$$l+lKseries=lK+lK$$  $$Kseries=$$ K     when rods are in parallel , effective coefficeint of thermal conductivity is   $$Kparallel=K1+K22$$   $$Kparallel=K+K2$$   $$Kparallel=$$ K  when rods are taken in parallel, amount of heat that flows in time $$t2$$ $$isQ2=Kparallel2A($$θ$$1-$$θ$$2)lt2----(2)$$  to find $$t2$$ equate $$eqn(1)$$ and $$eqn(2)Q1=Q2$$  $$KseriesA($$θ$$1-$$θ$$2)2lt1=Kparallel2A($$θ$$1-$$θ$$2)lt2$$  here $$Kseries=Kparallel$$  on solving we get  $$t2=3$$ minutes      $$---(1)$$

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