The final temperature of the glass is 25.005⁰C
Linear expansivity is defined as the change in length of an object per unit length per degree rise in temperature. Mathematically:
[tex]\alpha=\frac{\triangle L}{L\triangle \theta} \\\alpha = \frac{L_2-L_1}{L_1)(\theta_f-\theta_i)}[/tex]
where:
L2 is the final length = 500.9cm
L1 is the original length = 500cm
θf is the final temperature
θi is the initial temperature of the glass = 25°C
Linear expansivity of glass = 9 × 10⁻⁶
Substitute the given values into the formula as shown:
[tex]9 \times 10^{-6}=\frac{500.9-500}{500(\theta_f-25)} \\9 \times 10^{-6}=\frac{0.9}{500(\theta_f-25)} \\0.0045=\frac{0.9}{\theta_f-25}\\\frac{0.0045}{0.9}=\theta_f-25\\ 0.005=\theta - 25\\\theta = 25 + 0.005\\\theta = 25.005^0C[/tex]
Hence the final temperature of the glass is 25.005⁰C
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