Two rods A and B are of equal lengths. Each rod has the
ends at temperatures T1, and T2 . What is the condition that
will ensure equal rates of flow of heat through the rods
A and B?
Answers
Answered by
8
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 ) / L₂
It 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 / A₂
Therefore , the required condition is [ k₂ / k₁ = A₁ / A₂ ]
Similar questions