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In Fig. 18-44a, two identical rectangular rods of metal are welded end to end, w

ID: 2016808 • Letter: I

Question

In Fig. 18-44a, two identical rectangular rods of metal are welded end to end, with a temperature of T1 = 3°C on the left side and a temperature of T2 = 107°C on the right side. In 2.6 min, 77 J is conducted at a constant rate from the right side to the left side. How much time (in minutes) would be required to conduct 69 J if the rods were welded side to side as in Fig. 18-44b?

In Fig. 18-44a, two identical rectangular rods of metal are welded end to end, with a temperature of T1 = 3 degree C on the left side and a temperature of T2 = 107 degree C on the right side. In 2.6 min, 77 J is conducted at a constant rate from the right side to the left side. How much time (in minutes) would be required to conduct 69 J if the rods were welded side to side as in Fig. 18-44b?

Explanation / Answer

Given that the energy transfered when the rods are welded end to end is Q1 = 77J Time taken t1 = 2.6 min ----------------------------------------------------------------- Let the length of the each rod is L And A be the cross-sectional area of the each rod. Rate of heat energy transfered in the rod as shown in figure (a) is               P = kAT / L               P A/L In case (a)               Pa A/2L In case (b)               Pb 2A/L Then the ratio is           Pa / Pb = (A/2L) / (2A/L)                        = 1/4                   Pb = 4 Pa              Q2/t2  = 4 Q1/t1                     t2 = Q2*t1 / 4*Q1                          = 69J *2.6 min / 4*77J                          = 0.582 min                                                    In case (b)               Pb 2A/L Then the ratio is           Pa / Pb = (A/2L) / (2A/L)                        = 1/4                   Pb = 4 Pa              Q2/t2  = 4 Q1/t1                     t2 = Q2*t1 / 4*Q1                          = 69J *2.6 min / 4*77J                          = 0.582 min                                                                                                              

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