Three rods of same dimensions have thermal conductivities 3 K , 2 K and K . They are arranged as shown in the figure below. Then in the steady state the temperature of the junction P is

Step-by-step solution

Amount of heat transmitted from one point to another is Q= k A t (T₁-T₂ ) d where, k is thermal conductivity, t is time and T₁-T₂ is temperature difference. At junction, aligned Q & =Q₁+Q₂ 3 k A(100-T) t d & = 2 k A(T-50) t d + k A(T-0) t d 300 k A t-3 k A t T & =2 k A t T-100 k A t+k A T t 400 k A t & =6 k A t T T & = 400 6 T & = 200^ 3 C aligned