A rectangular piece of iron measuring 4 cm by 3 cm at 20\(^o\)C is heated until its temperature increases by 100 C. Calculate the new area of the metal. [Linear expansivity of iron is 1.2x 10\(^{-5}\) K\(^{-1}\)]
A. 12.0144 cm\(^3\) B. 12.0346 cm\(^3\) C. 12.0288 cm\(^3\) D. 12.0173 cm\(^3\)
Correct Answer: C
Explanation
Linear expansivity (\(\alpha\)) = \(\frac{A_2 - A_1}{A_1\theta}\) Original Area(A\(_1\)) = 4 x 3 = 12 New Area (A\(_2\)) = ? Temp. rise (\(\theta\)) = 100\(^o\)C A\(_2\) - 12 = 1200 x 2 x 1.2 x 10\(^{-5}\) A\(_2\) - 12 = 2880 x 10\(^-5\) A\(_2\) - 12 = 0.0288 A\(_2\) = 12.0288 cm\(^2\)
