To understand thermal linear expansion in solid materials. most materials expand when their temperatures increase. such thermal expansion, which is explained by the increase in the average distance between the constituent molecules, plays an important role in engineering. in fact, as the temperature increases or decreases, the changes in the dimensions of various parts of bridges, machines, etc., may be significant enough to cause trouble if not taken into account. that is why power lines are always sagging and parts of metal bridges fit loosely together, allowing for some movement. it turns out that for relatively small changes in temperature, the linear dimensions change in direct proportion to the temperature. for instance, if a rod has length l0 at a certain temperature t0 and length l at a higher temperature t, then the change in length of the rod is proportional to the change in temperature and to the initial length of the rod: l−l0=αl0(t−t0),orδl=αl0δt.