A rod CD of thermal resistance 5.0 K W⁻¹ is joined at the middle C of an identical rod AB, as shown in the figure. The ends A, B and D are maintained at 100°C, 0°C and 25°C, respectively. Find the heat current in CD in W.
Physics · Mixed Chapter
JEE Main Practice

Question

A rod CD of thermal resistance 5.0 K W⁻¹ is joined at the middle C of an identical rod AB, as shown in the figure. The ends A, B and D are maintained at 100°C, 0°C and 25°C, respectively. Find the heat current in CD in W.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Identical rods have total thermal resistance 5 K W⁻¹. Each half AC and CB of AB has 2.5 K W⁻¹. Step 2: Let junction temperature at C be Tₙ °C. Heat entering from A = (100 − Tₙ)/2.5 W. Step 3: Heat leaving toward B = Tₙ/2.5 W. Heat leaving toward D = (Tₙ − 25)/5 W. Step 4: Thermal balance at C: (100 − Tₙ)/2.5 = Tₙ/2.5 + (Tₙ − 25)/5. Step 5: Multiplying by 5 gives 2(100 − Tₙ) = 2Tₙ + (Tₙ − 25). Therefore 225 = 5Tₙ and Tₙ = 45°C. Step 6: Heat current H₍CD₎ = (45 − 25)/5 = 4 W. Final answer…