A solid material of volume 100\(cm^{-3}\) is heated through a temperature difference of 40°C. Calculate...

WAEC 1997

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\(10^{-2}cm^{-3}\)

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Correct Answer: Option A

Explanation

\(3{\alpha}= \frac{\Delta{V}}{V_1\Delta{T}}\Rightarrow \frac{\Delta{V}}{100\times40}=3\alpha\, where\, \alpha = 2 \times 10^{-6}\\ \frac{\Delta{V}}{4000}=6\times10^{-6}\Rightarrow \Delta=4\times10^3\times6\times10^{-6}= 2.4\times10^{-2}cm^{-3}\)

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