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: Option C
Explanation
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)