Rods of copper, brass and steel are welded together to form a Y-shaped figure. The cross-sectional area of each rod is 2.0 cm2 . The free end of the copper rod is maintained at 100◦C, and the free ends of the brass and steel rods at 0 ◦C. Assume there is no heat loss from the surface of the rods. The lengths of the rods are: copper, 13 cm; brass, 18 cm; steel, 24 cm. The thermal conductivities are: copper, 385 W m−1 K −1 ; brass, 109 W m−1 K −1 ; steel, 50.2 W m−1 K −1
(a)What is the temperature of the junction point?
(b)What is the heat current in each of the three rods?
H = kA (TH - TC)/L
The Attempt at a Solution
(a) I assumed that the heat flow through all 3 rods was the same:
kc (100 - T)/Lc = kb (T - 0.0)/Lb = ks (T - 0.0)/Ls
Lb kc (100 - T) = Lc kb]T
And with rearranging:
T = (100Lbkc)/(Lckb + Lbkc) = 83.0◦C
Is this correct? Can I just assume that heat flow is the same and ignore the steel rod?
(b) Do i just used: H = kA (TH - TC)/L again but for each metal? Because H = dQ/dt?
Copper: dQ/dt = (385)(2 x 10-4)(100-83)/0.13 = 10.1