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Two rods A and B are of equal lengths. Each rod has the ends at temperatures T1, and T2 . What is the condition thatwill ensure equal rates of flow of heat through the rodsA and B? |
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Answer» We KNOW : Rate of flow of heat is equal : = > Δ Q_A / Δ t = Δ Q_B/ Δ t APPLYING Newton law of cooling i.e. d T / d t = - K ( T - T₀ ) = > k₁ A₁ ( T₁ - T₂ ) / L₁ = k₂ A₂ ( T₁ - T₂ ) / L₂It is given that length are equal : L₁ = L₂= > k₁ A₁ ( T₁ - T₂ ) = k₂ A₂ ( T₁ - T₂ ) CLEARLY ( T₁ - T₂ ) GET cancel out : = > k₁ A₁ = k₂ A₂= > k₂ / k₁ = A₁ / A₂Therefore , the REQUIRED condition is [ k₂ / k₁ = A₁ / A₂ ] |
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