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 T_1 and that at the right junction is T_2. The ratio T_1 / T_2 is
C. 5 3
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
Related: Physics — Thermal Properties of Matter · All PYQ Banks