Question

An iron rail is 20m long. How much will it expand when heated from 100c to 500c (linear expansivity of Iron = 1.2x10-5 0c-1)

Answer 1

Given, $L_0=20m$ ,$T_i=100C,T_f=500C$,thus $\Delta T=T_f-T_i=400K$.

$\Delta L=L-L_0,\& \alpha_L=1.2 \times 10^{-5}K^{-1}$ ,

We know that

$$L=L_0(1+ \alpha \Delta T)$$

Thus,

$$L=20(1+1.2\times 10^{-5}\times 400)\\ \implies L =20.096m$$

Therefore, expansion of length is $\Delta L=0.096m$