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Question
Three rods of lengths 20 cm each and area of cross section 1 cm2 are joined to form a triangle ABC. The conductivities of the rods are KAB = 50 J s−1 m−1°C−1, KBC = 200 J s−1m−1°C−1 and KAC = 400 J s−1 m−1°C−1. The junctions A, B and C are maintained at 40°C, 80°C and 80°C respectively. Find the rate of heat flowing through the rods AB, AC and BC.
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Solution
Thermal conductivity of rod AB, KAB = 50 J/m-s-°C
Temperature of junction at A, TA = 40°C
Thermal conductivity of rod BC, KBC = 200 J/m-s-°C
Temperature of junction at B, TB = 80°C
Thermal conductivity of rod BC, KCA = 400 J/m-s-°C
temperature of junction at C, TC = 80°C
l = 20 cm = 20 × 10−2 m
A = 1 cm2 = 10−4 m2
(a) `(DeltaQ)_{AB}/(Deltat) = (K_{AB^A}(T_B - T_A))/l`
`=( 50 xx1xx10^-4 (40))/(20xx10^-2)`
= 1 W
(b) `(DeltaQ_{AC})/(Deltat) =( K_{AC^-A}(T_C - T_A))
/(20xx10^2)`
= 8 w
( c ) `(DeltaQ)_{BC)/ (Deltat) = ((K_{BC})^6A(T_B - t_c))/l`
= 0
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