Rate of flow of heat through a cylindrical rod is ' H ₁ '. The temperature at the ends of the rod are ' T₁ ' and ' T₂ '. If all the dimensions of the rod become double and the temperature difference remains the same, the rate of flow of heat becomes ' H ₂ '. Then

Step-by-step solution

Let l₁ be the initial length of the rod and r ₁ be the radius of the rod. Then. H ₁= kA ₁ ( ~T ₂- T ₁ ) l₁ After doubling the dimensions, H ₂= kA ₂ ( ~T ₂- T ₁ ) l₂ array ll & H ₂ H ₁ = A ₂ ~A ₁ l₁ l₂ & If r ₂=2 r ₁, then A ₂=4 ~A ₁ & Also, l₂=2 l₁ & H ₂ H ₁ =4 1 2 =2 & H ₂=2 H ₁ array