Question

A bar of gold (bar A) is in thermal contact with a bar of copper (bar B) of the same length and area. One end of the compound bar is maintained at Th = 76.0 degree C while the opposite end is at 30.0 degree C. Find the temperature at the junction when the energy flow reaches a steady state. Your response differs from the correct answer by more than 10%. Double check your calculations.

Answer 1

We know that q = k A dT / s
where
q = heat transferred per unit time (W )
A = heat transfer area (m^2)
k = thermal conductivity of the material (W/m.K)
dT = Temperature difference across the material ( K) = T(hot) - T(cold)
s = material thickness (m)

Since heat transferred per unit time at the junction is the same

k(Pb)A (T2-T1) / s = q = k(Ag) A (T1-T3) / s

k(Pb)=(T2 - T1) = k(Ag)(T1-T3)
finally
T1= [k(Pb)T2 + k(Ag)T3]/[k(Pb)+ k(Ag)]
T1=[35 (76.0 + 273.15 ) + 429 (30.0 + 273.15)]/[35+429]=
T1= 306.6198 K or
T1= 33.46 C