Answer to Question #303009 in Molecular Physics | Thermodynamics for NICKO

Question

One of the tallest buildings in the world has a height of 1671 feet. Assume that this height was measured on a winter day when the temperature was 16°C. You could use the building as a sort of giant thermometer on a hot summer day by carefully measuring its height. Suppose you do this and discover that the building is 0.581 foot taller than its official height. What is the temperature, assuming that the building is in thermal equilibrium with the air and that its entire frame is made of copper?

Answer 1

The coefficient of linear expansion is $\alpha = 16.6\cdot{10^{-6\,\,\circ}}/C.$

The relative expansion of the building is $\dfrac{\Delta h}{h} = \dfrac{0.581}{1671} = 3.5\cdot10^{-4}.$

Also $\Delta h = h\cdot \alpha\cdot \Delta t,$ or $\dfrac{\Delta h}{h} = \alpha\cdot \Delta t,$

$\Delta t = \dfrac{\Delta h}{\alpha h} = \dfrac{3.5\cdot10^{-4}}{16.6\cdot10^{-6}} = 20.9^\circ\,\mathrm{C}.$

Therefore, the temperature is $16+ 20.9 = 36.9^\circ\,\mathrm{C}.$