Three rods AB, BC & BD of same length ℓ and cross-sectional area A are arranged as shown. The end D is immersed in ice whose mass is M. Heat is being supplied at constant rate of 200 Cal/sec from the

Question

Three rods AB, BC & BD of same length ℓ and cross-sectional area A are arranged as shown. The end D is immersed in ice whose mass is M. Heat is being supplied at constant rate of 200 Cal/sec from the end A. Find amount of melted ice (in gm) in time 40/3 minute. Given : Thermal conductivity k = 100 cal / m / sec / ∘ C , A = 10 cm 2 , ℓ = 1 m , Latent heat of fusion of ice is = 80 cal/gm.

TestHub · Accepted Answer

Let θ be temperature of B: 200 = ℓ 2 KA ( θ − 100 ) ​ + ℓ ( k /2 ) A ( θ − 0 ) ​ (substituting value of θ = 88 0 ∘ C ) The heat transferred to the ice through BD: Q = mL : ℓ ( K /2 ) A ( 880 − 0 ) ​ × t = m × 80 = 2 × 1 100 × 10 × 1 0 − 4 × 880 ​ × 3 40 × 60 ​ = m × 80 ⇒ m = 440 gm Answer: 440

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