Three identical heat conducting rods are connected in series as shown in the figure. The rods on the sides have thermal conductivity 2 K while that in the middle has thermal conductivity K . The left end of the combination is maintained at temperature 3 T and the right end at T . The rods are thermally insulated from outside. In steady state, temperature at the left junction is T₁ and that at the right junction is T₂

Step-by-step solution

aligned & In steady state ( dQ dt )₁= ( dQ dt )₂= ( dQ dt )₃ & 2 KA (3 ~T - T ₁ ) L = KA ( ~T ₁- T ₂ ) L = 2 KA ( ~T ₂- T ) L & 6 ~T -2 ~T ₁= T ₁- T ₂=2 ~T ₂-2 ~T & 6 ~T -2 ~T ₁= T ₁- T ₂ & 6 ~T + T ₂=3 ~T ₁ ....(i) & ~T ₁- T ₂=2 ~T ₂-2 ~T & 2 ~T -3 ~T ₂=- T ₁.....(ii) aligned Multiply equation (2) By ' 3 ' 6 ~T -9 ~T ₂=-3 ~T ₁ ....(iii) Equation (1) - (3) aligned & 10 ~T ₂=6 ~T ₁ & ~T ₁ ~T ₂ = 5 3 aligned