A brass cube,13.0 cm on a side,is raised in temperature by 239°C.The coefficient of volume expansion of brass is 57 × 10−⁶/C°.By what percentage is any one of the 13.0-cm edges increased in length? A)0.34% B)5.9% C)0.45% D)1.8% E)4.3%

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Quizplus · Accepted Answer

The coefficient of linear expansion ($\alpha$) can be found from the coefficient of volume expansion ($\beta$) by dividing it by 3, since $\beta = 3\alpha$. Thus, $\alpha = \frac{57 \times 10^{-6}}{3} = 19 \times 10^{-6} \, \text{°C}^{-1}$. The change in length ($\Delta L$) of an edge due to thermal expansion is given by $\Delta L = \alpha L_0 \Delta T$, where $L_0$ is the original length and $\Delta T$ is the temperature change. Substituting the given values: $\Delta L = 19 \times 10^{-6} \times 13.0 \times 239$, which gives a percentage increase ($\frac{\Delta L}{L_0} \times 100\% $) of approximately 0.45%.

A Brass Cube,13