Assume all temperatures to be exact. A steel cylinder of radius 4.7 cm and lengt

Question

Assume all temperatures to be exact. A steel cylinder of radius 4.7 cm and length 4.9 cm is placed in end-to-end thermal contact with a copper cylinder of the same dimensions. If the free ends of the two cylinders are maintained at constant temperatures of 92 degree C (steel) and 21 degree C (copper), how much heat will flow through the cylinders in 25 min? Assume k_steel = 46 J/(m middot s middot degree C) and k_cooper = 390 J/(m middot s middot degree C). Express your answer using two significant figures.

Explanation / Answer

Given that

radius r=4.7 cm

length L=4.9 cm

Ksteel=46 J/m.s.c

Kcopper =390 J/m.s.c

now we find the equivalent thermal conductivity

Keq=K1K2/K1+K2=46*390/390+46=41.15 J/m.s.C

now we find the amount of heat flow through the cylinder 25 min

the amount of heat flow Q=Keq*A[T1-T2]*t/L

=41.15*3.14*0.047^2*[92-21]*25*60/0.049

=680670.1 J

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