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245.


Problem 25.54 (RHK)


Two identical rectangular rods of metal are welded end to end as shown in Fig. a, and 10 J of heat flows through the rod in 2.0 min. We have to calculate the time for 30 J to flow through the rods if they are welded as shown in the Fig. b.


Solution:           Click For PDF Version

Let L be the length of each metal rod and A their cross-sectional area. Let k be the thermal conductivity of the metal of the rods. In the configuration shown in Fig.a

10 J of energy flows in 2.0 min. Temperature difference across the ends of the rods is 100 K.

From the equation of heat conduction we have

When the two rods are arranged in the configuration as shown in Fig b, the cross-sectional area is 2A and length is L. The rate of heat flow will be

Therefore, time in which 30 J will flow though the rods will be 1.5 minute.