Answer to Question #347709 in Differential Equations for Arvind

Question

A long thin steel railway tie is 10 yards at 60oF. What will be the length be when the temperature falls to -15oF?

Answer 1

Given:

$t_1=60\:{^\circ\rm F}=15.6\:{^\circ\rm C}$

$t_2=-15\:{^\circ\rm F}=-26.1\:{^\circ\rm C}$

$$l=l_0(1+\alpha \Delta T)$$

$$l={10\:\rm yd(1+11*10^{-6}*(-26.1-15.6))}\\=9.995\:\rm yd$$