At 0^ C , a circular hole of diameter 2.00 cm is made in an aluminium plate. Determine its diameter at 100^ C . Given for aluminium = 2.3 10⁻⁵ ^ C ⁻¹ .

Step-by-step solution

The expansion of a hole in a solid is identical to the expansion of the solid material itself. The diameter of the hole at temperature T is given by the formula for linear expansion: D_T = D₀ (1 + T) Given: D₀ = 2.00 cm = 2.3 10⁻⁵ ^ C ⁻¹ T = 100^ C - 0^ C = 100^ C Substituting the values: D₁₀₀ = 2.00 [1 + (2.3 10⁻⁵) 100] D₁₀₀ = 2.00 [1 + 0.0023] D₁₀₀ = 2.00 1.0023 = 2.0046 cm