Two cylindrical rods A and B made of different materials, are joined in a straight line. The ratio of lengths, radii and thermal conductivities of these rods are : L _ A L _ B = 1 2 , r _ A r _ B =2 and K _ A K _ B = 1 2 . The free ends of

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Two cylindrical rods A and B made of different materials, are joined in a straight line. The ratio of lengths, radii and thermal conductivities of these rods are : L _ A L _ B = 1 2 , r _ A r _ B =2 and K _ A K _ B = 1 2 . The free ends of rods A and B are maintained at 400 ~K , 200 ~K , respectively. The temperature of rods interface is ________ K, when equilibrium is established.

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aligned & R ₁= ₁ ~K ₁ ~A ₁ , R ₂= ₂ ~K ₂ ~A ₂ & dQ dt = T R & ( dQ dt )₁= ( dQ )₂ & 400- T R ₁ = T -200 R ₂ & 400- T T -200 = R ₁ R ₂ = ( ₁ ₂ ) ( r ₂ r ₁ )^2 K ₂ ~K ₁ & = 1 2 ( 1 2 )^2 2 & = ( 1 4 ) & 400- T T -200 = 1 4 & 1600-4 ~T = T -200 & 5 ~T =1800 & ~T =360 ~K aligned

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