The area of a square aluminum plate at 0 degrees is 10 ^ 4 cm2. To what temperature was the plate heated if its area became equal to 10046.05 cm2
Data: S0 – the initial area of the taken aluminum plate (S0 = 104 cm2); S – steady-state area (S = 10046.05 cm2).
Const: α – coeff. thermal expansion of aluminum (at 0 ºС α = 22.8 * 10-6).
To find out the final temperature of the taken aluminum plate, we use the formula: l = l0 * (1 + α * (t – 0)), whence we express: t = (l / l0 – 1) / α = (√S / √S0 – 1 ) / α.
Let’s calculate: t = (√S / √S0 – 1) / α = (√10046.05 / √104 – 1) / (22.8 * 10-6) ≈ 100.87 ºС.
Answer: The taken aluminum plate was heated to 100.87 ºС.
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