A solid material of volume 100\(cm^{-3}\) is heated through a temperature difference of 40°C. Calculate the increase in the volume of the material if its linear expansitivity is 2 x \(10^{-6}K{-1}\)
A
2.4 x\(10^{-2}cm^{-3}\)
B
1.6 x\(10^{-2}cm^{-3}\)
C
8 x\(10^{-2}cm^{-3}\)
D
5 x\(10^{-2}cm^{-3}\)
E
4 x\(10^{-2}cm^{-3}\)
Verified Correct Answer: A.
Physical Principles & Numerical Solution
\(3{\alpha}= \frac{\Delta{V}}{V_1\Delta{T}}\Rightarrow \frac{\Delta{V}}{100\times40}=3\alpha\, where\, \alpha = 2 \times 10^{-6}\\ \frac{\Delta{V}}{4000}=6\times10^{-6}\Rightarrow \Delta=4\times10^3\times6\times10^{-6}= 2.4\times10^{-2}cm^{-3}\)
Source: Myschool Past Questions Archive (Record #26301)