A metal sheet of area 100cm\(^2\) was heated through 70°C. Calculate its new area if the linear expansivity of the metal is 0.000017K\(^{-1}\).

A.

100.06 cm2

B.

100.12cm2

C.

100.24cm2

D.

100.36cm2

Correct answer is C

Formula: A\(_2\) = A\(_1\)(1 + \(\beta \theta\))

where \(\beta\) = The area expansivity

\(\theta\) = Change in temperature.

\(\beta\) = 2\(\alpha\)

where \(\alpha\) = linear expansivity of the body.

⇒ \(\beta\) = 2 x 0.000017 

= 0.000034 K\(^{-1}\)

\(\therefore\) A\(_2\) = 100 (1 + (0.000034 x 70))

= 100(1 + 0.00238)

= 100(1.00238)

= 100.238 cm\(^2\)

= 100.24 cm\(^2\) (to 2 d.p)