Question

Two rods having thermal conductivity in the ratio of 5:3 having equal lengths and equal cross-sectional area are joined end to end. If the temperature of the free end of the first rod is 100°C and free end of the second rod is 20°C, then the temperature of the junction is?

(a) 50°C

(b) 70°C

(c) 60°C

(d) 90°C

Answer 1

Right answer is (b) 70°C

For explanation: Let T be the temperature of the junction. In the steady state,

Q1/t=Q2/t

(K1 A(100-T))/d=(K2 A(T-T2))/d

5(100-T)=3(T-20)

8T=560 or T=70°C.