A circular hole in an aluminum plate is$\mathbf{2}\mathbf{.}\mathbf{725}\mathbf{}\mathit{c}\mathit{m}$in diameter at $\mathbf{0}\mathbf{.}\mathbf{000}\mathbf{°}\mathit{C}$.What is its diameter when the temperature of the plate is raised to$\mathbf{100}\mathbf{.}\mathbf{0}\mathbf{°}\mathit{C}$?

• i) Diameter of the circular hole is $D_0=2.725cmor2.725\times {10}^{-2}mat{T}_I=0.0°C$
• ii) Final temperature is$T_f=100.0°C$

Find the change add it to the original diameter, to determine the diameter of a circular hole in an aluminum plate when the temperature in the diameter of the circular hole using the formula for linear expansion. Then of the plate is raised to$100.0°C$.

Formula:

The linear expansion of a body as follows:

$∆L=L\alpha ∆T$ …… (i)

Change in the diameter of the circular hole is due to linear expansion.

From equation (i), write the change in the diameter of aluminum circular hole as:

$∆D=D_0{\alpha }_{Al}∆T$

Here,$$\begin{gathered} ∆T=100-0=100°C \\ {\alpha }_{Al}=23\times {10}^{-6}/{}^{°}C \end{gathered}$$

Hence, the change in diameter is given using the values as:
$$\begin{gathered} ∆D=2.725\times {10}^{-2}\times 23\times {10}^{-6}\times \left(100\right) \\ =62.675\times {10}^{-6}m \\ =62.675\times {10}^{-4}cm \end{gathered}$$

Final diameter is the original diameter plus the change in the diameter. Hence, it is given as:
$$\begin{gathered} D=D_0+∆D \\ =2.725cm+62.675\times {10}^{-4}cm \\ =2.731cm \end{gathered}$$

Hence, the value of the final diameter after temperature raise is 2.731 cm.