what is the rate of heat trasfer through this combination? how much heat passes
ID: 2240099 • Letter: W
Question
what is the rate of heat trasfer through this combination?
how much heat passes the interface between a and b in 6.0s?
A) 332 K
B) 306 K
C) 296 K D) 323 K E) 313 K Two bars, A and B, each of length 2.0 m and cross sectional area 1.0 m2,are placed end to end as shown in the figure. The thermal conductivities of the bars are kA = 439 J/(s ? m ? K)and kB = 887 J/(s ? m ? K),respectively. The left end of bar A is maintained at 373 K while the right end of B is maintained at 273 K. What is the temperature at the interface between A and B? what is the rate of heat trasfer through this combination? how much heat passes the interface between a and b in 6.0s?
Explanation / 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] = [837 J/(s ? m ? K)] [Tf - 273 K]
where Tf = interface temp.
Tf = 354,948 / 1176 = 302 K
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