A bore made in an aluminium block at 34ºC is 3.48cm\(^3\). What is the new bore when the temperature was raised to 340ºC [\alpha\(_a\) = 24 x 10\(^{-6}\)K\(^{-1}\)]
A
4.14cm\(^3\)
B
3.83cm\(^3\)
C
3.56cm\(^3\)
D
3.24cm\(^3\)
Verified Correct Answer: C.
Physical Principles & Numerical Solution
\(\gamma\) = 3 \(\alpha\)
\(\gamma\) = 3 x 24 x 10\(^{-6}\) = 72 x 10\(^{-6}\)k\(^{-1}\)
V\(_2\) = V\(_1\)(1 + \(\gamma\) ∆T)
V\(_2\) = 3.48 x (1 + 72 x 10\(^{-6}\)k\(^{-1}\) x 306)
V\(_2\) = 3.48 x (1 + 0.022032)
V\(_2\) ≈ 3.56cm\(^3\)
Source: Myschool Past Questions Archive (Record #74553)