Three rods AB, BC and BD made of the same material and having the same area of cross section have been joined as shown in the figure. The ends A, C and D are held at temperature $20^{0}, 80^{0}$ and $80^{0} C$ respectively. If each rod is of same length, then find the temperature at the junction B of the three rods

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$θ_{B} = 40^{0} C$

$θ_{B} = 80^{0} C$

$θ_{3} = 60^{0} C$

$θ_{B} = 50^{0} C$

answer is C.

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Detailed Solution

${(\frac{θ}{t})}_{D B} + {(\frac{Q}{t})}_{C B} = {(\frac{Q}{t})}_{B A}$ $\frac{K A (80 - θ_{B})}{l} + \frac{K A (80 - θ_{B})}{l} = \frac{K A (θ_{B} - 20)}{l}$

$80 - θ_{B} + 80 - θ_{B} = θ_{B} - 20$

$θ_{B} = 60^{0} C$

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