The temperature difference across two cylindrical rods A and B of same material and same mass are 40^ C and 60^ C respectively. In steady state, if the rates of flow of heat through the rods A and B are in the ratio 3: 8 , the ratio of the lengths of the rods A and B is

Step-by-step solution

For rod A , T ₁=40^ C For rod B, T₂=60^ C Q _ A Q _ B = 3 8 ~A ₁ ~T ₁ l₁ ~A ₂ ~T ₂ l₂ = 3 8 ....(i) Also, m ₁= m ₂ ₁^ V ₁= ₂ ~V ₁= V ₂ A ₁ l₁= A ₂ l₂ ~A ₁ ~A ₂ = l₂ l₁ .....(ii) From eq(i) and (ii), we get ( T ₁ ~T ₂ ) ( l₂ l₁ )^2= 3 8 ( 40 60 ) ( l₂ l₁ )^2= 3 8 l₁: l₂=4: 3