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\(^3\)
Verified Correct Answer: C.
Physical Principles & Numerical Solution
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\(^2\)
Source: Myschool Past Questions Archive (Record #59017)