Question

Four identical rods AB, CD, CF and DE are joined as shown in figure. The length, cross-sectional area and thermal conductivity of each rod are l, A and K respectively. The ends A, E and F are maintained at temperature `T_(1)` , `T_(2)` and `T_(3)` respectively. Assuming no loss of heat to the atmospere, find the temperature at B.

Answer 1

Correct Answer - A::B::C
Let the tempareture at B be T
`(Q_A/t)=(Q_B/t)+(Q_C/t)`
`implies(KA(T-T_1))/l=(KA(T-T_2))/(l+l//2)+(KA(T-T_3))/(3l//2)`
`(T-T_1))/l=(T-T_2))/(l+l//2)+(T-T_3))/(3l//2)`
`implies T-T_1=(2/3)(2T-T_2-T_3)`
`implies3T=3T_1=4T-2(T_2+T_3)`
`implies-7=+3T_1-2(T_2+T_3)`
`impliesT=(-3T+2(T_2+T_3))/7`