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Question:

A composite block is made of slabs A, B, C, D, and E of different thermal conductivities (given in terms of a constant K) and sizes (given in terms of length, L) as shown in Fig. All slabs are of the same width. Heat flow through A and E slabs are the same. Heat flow through slab E is maximum. Temperature difference across slab E is smallest. Heat flow through C = heat flow through B + heat flow through D.

Heat flow through slab E is maximum

Heat flow through C = heat flow through B + heat flow through D

Heat flow through A and E slabs are the same

Temperature difference across slab E is smallest

Solution:

a. At steady state, heat flow through A and E are the same. So option (a) is correct and option (b) is incorrect.
c. ΔT = H × R, where H is heat current. 'H' is the same for A and E but R is smallest for E. So the temperature difference across slab E is smallest. So option (c) is correct.
d. HB = ΔTRB, HC = ΔTRC and HD = ΔTRD, From this option if, HC = HB + HD ⇒ 1/RC = 1/RB + 1/RD ⇒ 4K(2Kb)/4L = 2K(Lb)/4L + 5K(Lb)/4L which is true. Here b is the width of the slab. Hence option (d) is also correct.