the coefficient of linear expansion of a metal is 1×10^-5 the percentage increase in the area of the metal when it is heated through 100 degree Celsius is ??
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Answer:
it is given that,
coefficient of linear expansion, α = 10^-5 /°C
change in temperature, ∆T = (100°C - 0°C) = 100°C
we know, area of square is A = a²
area after increasing temperature , ∆T
A' = a²(1 + α∆T)²
as 1 >>> α∆T
so, (1 + α∆T)² ≈ 1 + 2α∆T
so, A' = a²(1 + 2α∆T)
now, change in area, ∆A = (A' - A)
= a²[1 + 2α∆T - 1]
= 2α∆T
now, percentage change = ∆A/A × 100
= 100 × 2α∆T
= 100 × 2 × 10^-5 × 100
= 0.2 %
Explanation:
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