Question

The average coefficient of linear expansion of copper is 1.7 10-5 (°c)−1. the statue of liberty is 93 m tall on a summer morning when the temperature is 25°c. assume the copper plates covering the statue are mounted edge to edge without expansion joints and do not buckle or bind on the framework supporting them as the day grows hot. what is the order of magnitude of the statue's increase in height?

Answer 1

`\Delta L \approx 0.024\,m`

Step-by-step explanation:

The average coefficient of linear expansion observes the following approximation:

`\bar \alpha \approx (1)/(L)\cdot (\Delta L)/(\Delta T)`

Maximum temperature in New York during summer can reach up to 40 °C. The increase in height is:

`\Delta L \approx \alpha \cdot L \cdot \Delta T`

`\Delta L \approx \left(1.7* 10^(-5)\,(1)/(^(\textdegree)C) \right)\cdot (93\,m)\cdot (40\,^(\textdegree)C-25\,^(\textdegree)C)`

`\Delta L \approx 0.024\,m`

Answer 2

Let the rise in temperature be
`5^0C`

The expansion in length due to change in temperature is given by the expression lαΔt , where l is the length, α is the coefficient of linear expansion, Δt is the change in temperature.

Here l = 93 m, α =
`1.7*10^(-5)`
`^0C^(-1)`, and Δt =
`5^0C`

So expansion in length = 93*
`1.7*10^(-5)`*5 = 0.007905 m =
`0.79*10^(-3)m`

So order of magnitude in change in length = -3