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Two rods of diffrent material with diffrent area of cross section and length of second rod is equal to twice of length of first rod, k 2 =4k 1 and diameter of d 2 =d 1 /2 where d is the diameter if two conductors . Find the Temperature at the junction

Two rods of diffrent material with diffrent area of cross section and length of second rod is equal to twice of length of first rod, k2=4k1 and diameter of d2=d1/2 where d is the diameter  if two conductors . Find the Temperature at the junction 

Grade:11

1 Answers

Eshan
askIITians Faculty 2095 Points
5 years ago
Dear student,

For rods connected end to end, the rate of heat transfer through them must be same.

Hence\dfrac{K_1A_1}{l_1}(T_A-T)=\dfrac{K_2A_2}{l_2}(T-T_B)
\implies \dfrac{K_1\pi d_1^2}{4l_1}(T_A-T)=\dfrac{K_2\pi d_2^2}{4l_2}(T-T_B)
\implies 2(T_A-T)=(T-T_B)
\implies T=\dfrac{2T_A+T_B}{3}

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