The temperature of a metal strip having coefficient of linear expansion is increased from T₁ to T₂ resulting in increase of its length by L₁ . The temperature is further increased from T₂ to T₃ such that the increase in its length is L₂ . Given T₃+T₁=2T₂ and T₂-T₁= T , the value of L₂ is ______.

Step-by-step solution

Let the length of the metal strip at temperature T₁ be L₁ . When the temperature is increased from T₁ to T₂ , the new length L₂ is given by: L₂ = L₁(1 + T) where T = T₂ - T₁ . The increase in length is: L₁ = L₂ - L₁ = L₁ T When the temperature is further increased from T₂ to T₃ , the new length L₃ is: L₃ = L₂(1 + T') where T' = T₃ - T₂ . Given T₃ + T₁ = 2T₂ , we have T₃ - T₂ = T₂ - T₁ = T . Thus, T' = T . The increase in length for this second temperature change is: L₂ = L₃ - L₂ = L₂ T Substituting L₂ = L₁(1 + T) i