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Q.

Each side of a box is made of metal sheet in cubic shape ‘a’ at room temperature ‘T’, the coefficient of linear expansion of the metal sheet is ‘ $α$ ’. The metal sheet is heated uniformly, by a small temperature $Δ T$ , so that its new temperature is $T + Δ T$ . Then increase in the area of the metal box is

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a

$12 a^{2} α Δ T$

b

$8 a^{2} α Δ T$

c

$4 a^{2} α Δ T$

d

$2 a^{2} α Δ T$

answer is A.

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Detailed Solution

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$Δ A = A β Δ T, Δ A = 6 a^{2} 2 α Δ T = 12 a^{2} α Δ T$

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Each side of a box is made of metal sheet in cubic shape ‘a’ at room temperature ‘T’, the coefficient of linear expansion of the metal sheet is ‘ α’. The metal sheet is heated uniformly, by a small temperature ΔT, so that its new temperature is T+ΔT. Then increase in the area of the metal box is