Question

The coefficient of linear expansion of a metal is 1×10−5/∘C . The percentage increase in area of a square plate of that metal when it is heated through 100∘C is​

Answer 1

percentage change in area of square is 0.2%

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 %

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Answer 2

$\huge\bold\purple{Answer:-}$

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 %