Answer to Question #241363 in Physics for Alvin

Question

A steel beam 12.0m sits next to a concrete wall when the temperature is 20.0°C.

A gap must be left between the beam and the concrete wall for expansion

purposes. If the temperature rises to 45.0°C, how large must the gap be if the

steel beam just touches the concrete wall?

Answer 1

Given:

$l_0=12.0\: \rm m$

$\alpha=12.0*10^{-6}\: \rm K^{-1}$

$\Delta t=25\:\rm K$

The size of a gap

$$\Delta l=l_0*\alpha\Delta t\\=12.0\:\rm m*12.0*10^{-6}\: K^{-1}*25\: K=0.0036\: m=3.6\: mm$$