QuestionJuly 21, 2025

1) The height of the Washington Monument is measured to be 170 m on a day when the temperature is 35.0^circ C What will its height be on a day when the temperature falls to -10.0^circ C Although the monument is made of limestone, assume that its thermal coefficient of expansion is the same as marble's.

1) The height of the Washington Monument is measured to be 170 m on a day when the temperature is 35.0^circ C What will its height be on a day when the temperature falls to -10.0^circ C Although the monument is made of limestone, assume that its thermal coefficient of expansion is the same as marble's.
1) The height of the Washington Monument is measured to be 170 m on a day when the temperature is 35.0^circ C What will its height be on a day when the temperature falls to -10.0^circ C Although the monument is made of limestone, assume that its thermal coefficient of expansion is the same as marble's.

Solution
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Answer

169.980875 m Explanation 1. Identify the thermal expansion formula The change in length due to temperature is given by **\Delta L = \alpha L_0 \Delta T**, where \alpha is the coefficient of linear expansion, L_0 is the original length, and \Delta T is the change in temperature. 2. Determine the values Given: L_0 = 170 \text{ m}, \Delta T = -10.0^{\circ}C - 35.0^{\circ}C = -45.0^{\circ}C, and \alpha = 2.5 \times 10^{-6} \text{ } ^{\circ}C^{-1} (for marble). 3. Calculate the change in height Substitute into the formula: \Delta L = (2.5 \times 10^{-6})(170)(-45) = -0.019125 \text{ m}. 4. Calculate the new height New height = L_0 + \Delta L = 170 - 0.019125 = 169.980875 \text{ m}.

Explanation

1. Identify the thermal expansion formula<br /> The change in length due to temperature is given by **$\Delta L = \alpha L_0 \Delta T$**, where $\alpha$ is the coefficient of linear expansion, $L_0$ is the original length, and $\Delta T$ is the change in temperature.<br /><br />2. Determine the values<br /> Given: $L_0 = 170 \text{ m}$, $\Delta T = -10.0^{\circ}C - 35.0^{\circ}C = -45.0^{\circ}C$, and $\alpha = 2.5 \times 10^{-6} \text{ } ^{\circ}C^{-1}$ (for marble).<br /><br />3. Calculate the change in height<br /> Substitute into the formula: $\Delta L = (2.5 \times 10^{-6})(170)(-45) = -0.019125 \text{ m}$.<br /><br />4. Calculate the new height<br /> New height $= L_0 + \Delta L = 170 - 0.019125 = 169.980875 \text{ m}$.
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