Two bars, A and B, each of length 2.0 m and cross sectional area 1.0 m 2 , are p
ID: 2092691 • Letter: T
Question
Two bars, A and B, each of length 2.0 m and cross sectional area 1.0 m2, are placed end to end, with bar A being on the left and bar B being on the right. The thermal conductivities of the bars are kA = 439 J/(s Two bars, A and B, each of length 2.0 m and cross sectional area 1.0 m2, are placed end to end, with bar A being on the left and bar B being on the right. The thermal conductivities of the bars are kA = 439 J/(s Two bars, A and B, each of length 2.0 m and cross sectional area 1.0 m2, are placed end to end, with bar A being on the left and bar B being on the right. The thermal conductivities of the bars are kA = 439 J/(sExplanation / Answer
Q = k(A)(dT)(t) / L
where Q = heat conducted through ends of the bar
k = thermal conducitvity of the bar
A = bar cross-sectional area
dT = temperature difference between the ends of the bar
t = time duration
L = bar length
At the interface Q from bar A into bar B = Q from bar B into A
(ka)(Aa)(dTa)(ta) / (La) = (kb)(Ab)(dTb)(tb) / Lb
since the A's, t's, and L's are the same on each side of the eqn. you get:
(ka)(dTa) = (kb)(dTb)
[439 J/(s ? m ? K)] [ 373 K - Tf] = [887 J/(s ? m ? K)] [Tf - 273 K]
where Tf = interface temp.
Tf = 405898 / 1326 = 306.1 K
temperature at the interface between A and B is 306 K