Heat and Thermodynamics 3 Question 6

6. Three rods of copper, brass and steel are welded together to form a Y-shaped structure. Area of cross-section of each rod is 4cm2. End of copper rod is maintained at 100C whereas ends of brass and steel are kept at 0C. Lengths of the copper, brass and steel rods are 46, 13 and 12cm respectively.

The rods are thermally insulated from surroundings except at ends. Thermal conductivities of copper, brass and steel are 0.92,0.26 and 0.12 in CGS units, respectively. Rate of heat flow through copper rod is

(a) 1.2cal/s

(b) 2.4cal/s

(c) 4.8cal/s

(d) 6.0cal/s

(2014 Main)

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Solution:

  1. In thermal conduction, it is found that in steady state the heat current is directly proportional to the area of cross-section A which is proportional to the change in temperature (T1T2).

Then,

ΔQΔt=KA(T1T2)x

According to thermal conductivity, we get

 i.e. dQ1dt=dQ2dt+dQ3dt0.92(100T)46=0.26(T0)13+0.12(T0)12T=40CdQ1dt=0.92×4(10040)40

=4.8cal/s



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