The coefficient of linear expansion of aluminum is \(23 \times 10^{6} K ^{-1}\). If the volume of a pot made with aluminum at temperature \(T_{0}\) is \(V_{11}\), what will be the change in temperature resulting in a decrease of \(0.20 \%\) in volume of the pot?
A. \(-87^{\circ} C\) B. \(+487^{\circ} C\) C. \(+428^{\circ} C\) D. \(-29^{\circ} C\)
Correct Answer: D
Explanation
The original volume of the aluminium pot \(=V_{ o }\), Let the new volume \(=V\) Since there is a decrease of \(0.20 \%\) in volume, \(\begin{aligned} V &=V_{0}-\left(\frac{0.20}{100}\right) V_{0}=V_{0}-0.002 V_{0} \\ &=0.998 V _{0} \\ \gamma &=3 \alpha=3\left(2.3 \times 10^{-5}\right)=6.9 \times 10^{-5} \end{aligned}\)hange in temperature \(=\Delta T\) \(1=V_{0}(1+\gamma \Delta T )\) \(0.998) K =K\left(1+6.9 \times 10^{-5} \Delta T\right)\) \begin{aligned} \Delta T &=\frac{0.998-1}{6.9 \times 10^{-5}}=\frac{0.002}{6.9 \times 10^{-5}} \\ &=-28.980^{\circ} C \\ &=-20^{\circ} C \end{aligned}