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 minRelated Questions
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