NTA Abhyas JEE Main2020PhysicsThermal Properties of MatterPractice
Three rods AB , BC and BD of same length l and cross section A are arranged as shown. The end D is immersed in ice whose mass is 440 g and is at 0 ° C . The end C is maintained at 100 ° C . Heat is supplied at a constant rate of 200 cal s - 1 . Thermal conductivities of AB , BC and BD are K , 2 K and K / 2 , respectively. Time after which whole ice will melt is n × 10 2 s . What is the value of n ? ( K = 100 cal m
Correct answer
8
Step-by-step solution
Let θ be the temperature of B , then 2 KA θ - 1 0 0 l ⁡ + K 2 A θ - 0 l ⁡ = 2 0 0 Substituting the values we obtain, 2 θ - 200 + θ 2 = 2000 θ = 880   ° C Rate of heat flow from B to D K A 2 ( θ − 0 ) l = 0.1 2 ( 880 ) = 44   cal s - 1 t = 440 × 80 44 = 800   s ⇒ n = 8