Answer to Question #300422 in Physics for Sophia

Question

A metal rod of length 40.0cm at 20C is heated through a temperature of 45C.if the new length of the rod is 40.05cm calculate its linear expansivity

Answer 1

Given:

$l_0=40.00\;\rm cm$

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

$l=40.05\;\rm cm$

The thermal linear expansion is described by an equation

$$\Delta l=l_0\alpha\Delta T\\$$

Hence, the linear expansivity of a metal

$$\alpha=\frac{\Delta l}{l_0\Delta T}=\frac{0.05\:\rm cm}{40.00\:\rm cm*25\: K}=5*10^{-5}\: \rm K^{-1}$$